Portfolio
Total Employment in U.S.A In 2017
Spring 2020
Original Data Table
http://mathforum.org/workshops/sum96/data.collections/datalibrary/data.set6.html
| State FIPS | State | 116th Congressional District | 2017 NAICS Code | NAICS Description | Number of Establishments | Employment | Employment Noise Flag | 1st Quarter Payroll ($1,000) | 1st Quarter Payroll Noise Flag | Annual Payroll ($1,000) | Annual Payroll Noise Flag |
| 01 | Alabama | 01 | ------ | Total for all sectors | 15,921 | 244,615 | G | 2,492,282 | G | 10,417,508 | G |
| 01 | Alabama | 01 | 11---- | Agriculture, forestry, fishing and hunting | 142 | 1,127 | G | 10,591 | G | 44,855 | G |
| 01 | Alabama | 01 | 21---- | Mining, quarrying, and oil and gas extraction | 34 | 500 | G | 10,491 | H | 41,785 | H |
| 01 | Alabama | 01 | 22---- | Utilities | 56 | 1,618 | G | 46,260 | H | 151,722 | H |
| 01 | Alabama | 01 | 23---- | Construction | 1,367 | 16,277 | G | 194,035 | G | 855,500 | G |
| 01 | Alabama | 01 | 31---- | Manufacturing | 568 | 27,761 | G | 477,179 | G | 1,897,405 | G |
| 01 | Alabama | 01 | 42---- | Wholesale trade | 857 | 10,723 | G | 152,635 | G | 607,774 | G |
| 01 | Alabama | 01 | 44---- | Retail trade | 2,811 | 37,463 | G | 248,940 | G | 1,015,434 | G |
| 01 | Alabama | 01 | 48---- | Transportation and warehousing | 574 | 9,862 | G | 114,653 | G | 487,821 | G |
| 01 | Alabama | 01 | 51---- | Information | 284 | 4,229 | G | 64,288 | G | 254,116 | G |
| 01 | Alabama | 01 | 52---- | Finance and insurance | 1,184 | 9,273 | G | 139,135 | G | 589,963 | G |
| 01 | Alabama | 01 | 53---- | Real estate and rental and leasing | 867 | 4,411 | G | 39,547 | G | 172,784 | G |
| 01 | Alabama | 01 | 54---- | Professional, scientific, and technical | 1,432 | 12,406 | G | 201,202 | G | 828,587 | G |
| 01 | Alabama | 01 | 55---- | Management of companies and enterprises | 105 | 3,216 | G | 67,676 | G | 326,639 | H |
| 01 | Alabama | 01 | 56---- | Administrative and support and waste | 776 | 20,049 | G | 142,193 | H | 624,241 | H |
| 01 | Alabama | 01 | 61---- | Educational services | 149 | 5,247 | H | 35,641 | H | 151,186 | H |
| 01 | Alabama | 01 | 62---- | Health care and social assistance | 1,418 | 32,773 | G | 336,896 | G | 1,468,707 | G |
| 01 | Alabama | 01 | 71---- | Arts, entertainment, and recreation | 207 | 3,514 | G | 12,609 | G | 55,387 | G |
| 01 | Alabama | 01 | 72---- | Accommodation and food services | 1,408 | 31,656 | G | 122,659 | G | 533,285 | G |
| 01 | Alabama | 01 | 81---- | Other services (except public administration) | 1,663 | 12,472 | G | 75,566 | G | 309,828 | G |
New Data Table
Dependent variable
Independent variables
Independent
Binary
Categorical
| State FIPS | State | 116th Congressional District | 2017 NAICS Code | NAICS Description | Number of Establishments | Employment | Employment Noise Flag | 1st Quarter Payroll ($1,000) | 1st Quarter Payroll Noise Flag | Annual Payroll ($1,000) | Annual Payroll Noise Flag |
| 01 | Alabama | 01 | ------ | Total for all sectors | 15,921 | 244,615 | G | 2,492,282 | G | 10,417,508 | G |
| 01 | Alabama | 01 | 11---- | Agriculture, forestry, fishing and hunting | 142 | 1,127 | G | 10,591 | G | 44,855 | G |
| 01 | Alabama | 01 | 21---- | Mining, quarrying, and oil and gas extraction | 34 | 500 | G | 10,491 | H | 41,785 | H |
| 01 | Alabama | 01 | 22---- | Utilities | 56 | 1,618 | G | 46,260 | H | 151,722 | H |
| 01 | Alabama | 01 | 23---- | Construction | 1,367 | 16,277 | G | 194,035 | G | 855,500 | G |
| 01 | Alabama | 01 | 31---- | Manufacturing | 568 | 27,761 | G | 477,179 | G | 1,897,405 | G |
| 01 | Alabama | 01 | 42---- | Wholesale trade | 857 | 10,723 | G | 152,635 | G | 607,774 | G |
| 01 | Alabama | 01 | 44---- | Retail trade | 2,811 | 37,463 | G | 248,940 | G | 1,015,434 | G |
| 01 | Alabama | 01 | 48---- | Transportation and warehousing | 574 | 9,862 | G | 114,653 | G | 487,821 | G |
| 01 | Alabama | 01 | 51---- | Information | 284 | 4,229 | G | 64,288 | G | 254,116 | G |
| 01 | Alabama | 01 | 52---- | Finance and insurance | 1,184 | 9,273 | G | 139,135 | G | 589,963 | G |
| 01 | Alabama | 01 | 53---- | Real estate and rental and leasing | 867 | 4,411 | G | 39,547 | G | 172,784 | G |
| 01 | Alabama | 01 | 54---- | Professional, scientific, and technical | 1,432 | 12,406 | G | 201,202 | G | 828,587 | G |
| 01 | Alabama | 01 | 55---- | Management of companies and enterprises | 105 | 3,216 | G | 67,676 | G | 326,639 | H |
| 01 | Alabama | 01 | 56---- | Administrative and support and waste | 776 | 20,049 | G | 142,193 | H | 624,241 | H |
| 01 | Alabama | 01 | 61---- | Educational services | 149 | 5,247 | H | 35,641 | H | 151,186 | H |
| 01 | Alabama | 01 | 62---- | Health care and social assistance | 1,418 | 32,773 | G | 336,896 | G | 1,468,707 | G |
| 01 | Alabama | 01 | 71---- | Arts, entertainment, and recreation | 207 | 3,514 | G | 12,609 | G | 55,387 | G |
| 01 | Alabama | 01 | 72---- | Accommodation and food services | 1,408 | 31,656 | G | 122,659 | G | 533,285 | G |
Binary
Categorical Variables
The categorical variable in this case is the 2017 NAICS Code ,
Binary variables included: the State FIPS and 116th Congregation
District
Categorical variables include State. North East will become my reference level.
| 2017 NAICS Code |
| ------ |
| 11---- |
| 21---- |
| 22---- |
| 23---- |
| 31---- |
| 42---- |
| 44---- |
| 48---- |
| 51---- |
| 52---- |
| 53---- |
| 54---- |
| 55---- |
| 56---- |
| 61---- |
| 62---- |
| 71---- |
| 72---- |
| State FIPS | 116th Congressional District |
| 01 | 01 |
| 01 | 01 |
| 01 | 01 |
| 01 | 01 |
| 01 | 01 |
| 01 | 01 |
| 01 | 01 |
| 01 | 01 |
| 01 | 01 |
| 01 | 01 |
| 01 | 01 |
| 01 | 01 |
| 01 | 01 |
| 01 | 01 |
| 01 | 01 |
| 01 | 01 |
| 01 | 01 |
| 01 | 01 |
| 01 | 01 |
| 01 | 01 |
4
Removing 3 Variables due to Multicollinearty
I removed Employment Noise Flag (Non-numeric)
I removed First Quarter Payroll Noise Flag (Non-numeric)
| State FIPS | State | 116th Congressional District | 2017 NAICS Code | NAICS Description | Number of Establishments | Employment | Employment Noise Flag | 1st Quarter Payroll ($1,000) | 1st Quarter Payroll Noise Flag | Annual Payroll ($1,000) | Annual Payroll Noise Flag |
| 01 | Alabama | 01 | ------ | Total for all sectors | 15,921 | 244,615 | G | 2,492,282 | G | 10,417,508 | G |
| 01 | Alabama | 01 | 11---- | Agriculture, forestry, fishing and hunting | 142 | 1,127 | G | 10,591 | G | 44,855 | G |
| 01 | Alabama | 01 | 21---- | Mining, quarrying, and oil and gas extraction | 34 | 500 | G | 10,491 | H | 41,785 | H |
| 01 | Alabama | 01 | 22---- | Utilities | 56 | 1,618 | G | 46,260 | H | 151,722 | H |
| 01 | Alabama | 01 | 23---- | Construction | 1,367 | 16,277 | G | 194,035 | G | 855,500 | G |
| 01 | Alabama | 01 | 31---- | Manufacturing | 568 | 27,761 | G | 477,179 | G | 1,897,405 | G |
| 01 | Alabama | 01 | 42---- | Wholesale trade | 857 | 10,723 | G | 152,635 | G | 607,774 | G |
| 01 | Alabama | 01 | 44---- | Retail trade | 2,811 | 37,463 | G | 248,940 | G | 1,015,434 | G |
| 01 | Alabama | 01 | 48---- | Transportation and warehousing | 574 | 9,862 | G | 114,653 | G | 487,821 | G |
| 01 | Alabama | 01 | 51---- | Information | 284 | 4,229 | G | 64,288 | G | 254,116 | G |
| 01 | Alabama | 01 | 52---- | Finance and insurance | 1,184 | 9,273 | G | 139,135 | G | 589,963 | G |
| 01 | Alabama | 01 | 53---- | Real estate and rental and leasing | 867 | 4,411 | G | 39,547 | G | 172,784 | G |
| 01 | Alabama | 01 | 54---- | Professional, scientific, and technical | 1,432 | 12,406 | G | 201,202 | G | 828,587 | G |
| 01 | Alabama | 01 | 55---- | Management of companies and enterprises | 105 | 3,216 | G | 67,676 | G | 326,639 | H |
| 01 | Alabama | 01 | 56---- | Administrative and support and waste | 776 | 20,049 | G | 142,193 | H | 624,241 | H |
| 01 | Alabama | 01 | 61---- | Educational services | 149 | 5,247 | H | 35,641 | H | 151,186 | H |
| 01 | Alabama | 01 | 62---- | Health care and social assistance | 1,418 | 32,773 | G | 336,896 | G | 1,468,707 | G |
| 01 | Alabama | 01 | 71---- | Arts, entertainment, and recreation | 207 | 3,514 | G | 12,609 | G | 55,387 | G |
| 01 | Alabama | 01 | 72---- | Accommodation and food services | 1,408 | 31,656 | G | 122,659 | G | 533,285 | G |
| 01 | Alabama | 01 | 81---- | Other services (except public administration) | 1,663 | 12,472 | G | 75,566 | G | 309,828 | G |
I removed Annual Noise Flag (Non-Numeric)
5
Keeping variables
The States variable is retained in this case since it facilitate easy reading of the model. Moreover, it helps in relating the given regions.
Employment variable was retained because it shows
the number of employment in a particular state
and therefore enable to compare regions.
Therefore, this variable is important.
Annual payroll is also retained because it provides
general information about the payment of a given category
of work.
| State | Employment | 1st Quarter Payroll ($1,000) | Annual Payroll ($1,000) |
| Alabama | 244,615 | 2,492,282 | 10,417,508 |
| Alabama | 1,127 | 10,591 | 44,855 |
| Alabama | 500 | 10,491 | 41,785 |
| Alabama | 1,618 | 46,260 | 151,722 |
| Alabama | 16,277 | 194,035 | 855,500 |
| Alabama | 27,761 | 477,179 | 1,897,405 |
| Alabama | 10,723 | 152,635 | 607,774 |
| Alabama | 37,463 | 248,940 | 1,015,434 |
| Alabama | 9,862 | 114,653 | 487,821 |
| Alabama | 4,229 | 64,288 | 254,116 |
| Alabama | 9,273 | 139,135 | 589,963 |
| Alabama | 4,411 | 39,547 | 172,784 |
| Alabama | 12,406 | 201,202 | 828,587 |
| Alabama | 3,216 | 67,676 | 326,639 |
| Alabama | 20,049 | 142,193 | 624,241 |
| Alabama | 5,247 | 35,641 | 151,186 |
| Alabama | 32,773 | 336,896 | 1,468,707 |
| Alabama | 3,514 | 12,609 | 55,387 |
| Alabama | 31,656 | 122,659 | 533,285 |
| Alabama | 12,472 | 75,566 | 309,828 |
Running the Multiple Regression
Alpha= 0.05
P-Value of Model=
2.08E-12
R= 0.99
Adjusted R squared= 0.97
Adjusted R squared is used instead of R Square because dealing with multiple regression, multiple variables calculated together will cause inflation in the model.
97% of the variance can be explained by the model.
| SUMMARY OUTPUT | ||||||||
| Regression Statistics | ||||||||
| Multiple R | 0.989512 | |||||||
| R Square | 0.979134 | |||||||
| Adjusted R Square | 0.97357 | |||||||
| Standard Error | 560.3778 | |||||||
| Observations | 20 | |||||||
| ANOVA | ||||||||
| df | SS | MS | F | Significance F | ||||
| Regression | 4 | 2.21E+08 | 55258993 | 175.971 | 2.08E-12 | |||
| Residual | 15 | 4710349 | 314023.3 | |||||
| Total | 19 | 2.26E+08 | ||||||
| Coefficients | Standard Error | t Stat | P-value | Lower 95% | Upper 95% | Lower 95.0% | Upper 95.0% | |
| Intercept | 80.18125 | 402.4224 | 0.199247 | 0.844746 | -777.562 | 937.9242 | -777.562 | 937.9242 |
| Emplyment | 0.071086 | 0.019462 | 3.65246 | 0.002358 | 0.029602 | 0.112569 | 0.029602 | 0.112569 |
| 1st Quarter payroll | -0.0062 | 0.01697 | -0.36561 | 0.719757 | -0.04237 | 0.029966 | -0.04237 | 0.029966 |
| Annual Payroll | 0.001318 | 0.004199 | 0.313769 | 0.758017 | -0.00763 | 0.010268 | -0.00763 | 0.010268 |
| 2017 NAICS | -1.18884 | 7.537925 | -0.15771 | 0.876785 | -17.2555 | 14.87787 | -17.2555 | 14.87787 |
| RESIDUAL OUTPUT | ||||||||
| Observation | Predicted Y | Residuals | ||||||
| 1 | 15732.2 | 188.803 | ||||||
| 2 | 140.6094 | 1.390577 | ||||||
| 3 | 80.72567 | -46.7257 | ||||||
| 4 | 81.94295 | -25.9429 | ||||||
| 5 | 1133.269 | 233.7314 | ||||||
| 6 | 1556.223 | -988.223 | ||||||
| 7 | 646.3199 | 210.6801 | ||||||
| 8 | 2484.405 | 326.5951 | ||||||
| 9 | 655.5826 | -81.5826 | ||||||
| 10 | 256.1365 | 27.86351 | ||||||
| 11 | 591.6482 | 592.3518 | ||||||
| 12 | 313.033 | 553.967 | ||||||
| 13 | 741.3139 | 690.6861 | ||||||
| 14 | 253.91 | -148.91 | ||||||
| 15 | 1379.104 | -603.104 | ||||||
| 16 | 358.7258 | -209.726 | ||||||
| 17 | 2181.151 | -763.151 | ||||||
| 18 | 240.3172 | -33.3172 | ||||||
| 19 | 2186.522 | -778.522 | ||||||
| 20 | 809.8647 | 853.1353 |
What is significant?
Alpha= 0.05
Employment variable has a p-value of 0.002358
| SUMMARY OUTPUT | ||||||||
| Regression Statistics | ||||||||
| Multiple R | 0.989512 | |||||||
| R Square | 0.979134 | |||||||
| Adjusted R Square | 0.97357 | |||||||
| Standard Error | 560.3778 | |||||||
| Observations | 20 | |||||||
| ANOVA | ||||||||
| df | SS | MS | F | Significance F | ||||
| Regression | 4 | 2.21E+08 | 55258993 | 175.971 | 2.08E-12 | |||
| Residual | 15 | 4710349 | 314023.3 | |||||
| Total | 19 | 2.26E+08 | ||||||
| Coefficients | Standard Error | t Stat | P-value | Lower 95% | Upper 95% | Lower 95.0% | Upper 95.0% | |
| Intercept | 80.18125 | 402.4224 | 0.199247 | 0.844746 | -777.562 | 937.9242 | -777.562 | 937.9242 |
| Employment | 0.071086 | 0.019462 | 3.65246 | 0.002358 | 0.029602 | 0.112569 | 0.029602 | 0.112569 |
| 1st Quarter payroll | -0.0062 | 0.01697 | -0.36561 | 0.719757 | -0.04237 | 0.029966 | -0.04237 | 0.029966 |
| Annual Payroll | 0.001318 | 0.004199 | 0.313769 | 0.758017 | -0.00763 | 0.010268 | -0.00763 | 0.010268 |
| 2017 NAICS | -1.18884 | 7.537925 | -0.15771 | 0.876785 | -17.2555 | 14.87787 | -17.2555 | 14.87787 |
| RESIDUAL OUTPUT | ||||||||
| Observation | Predicted Y | Residuals | ||||||
| 1 | 15732.2 | 188.803 | ||||||
| 2 | 140.6094 | 1.390577 | ||||||
| 3 | 80.72567 | -46.7257 | ||||||
| 4 | 81.94295 | -25.9429 | ||||||
| 5 | 1133.269 | 233.7314 | ||||||
| 6 | 1556.223 | -988.223 | ||||||
| 7 | 646.3199 | 210.6801 | ||||||
| 8 | 2484.405 | 326.5951 | ||||||
| 9 | 655.5826 | -81.5826 | ||||||
| 10 | 256.1365 | 27.86351 | ||||||
| 11 | 591.6482 | 592.3518 | ||||||
| 12 | 313.033 | 553.967 | ||||||
| 13 | 741.3139 | 690.6861 | ||||||
| 14 | 253.91 | -148.91 | ||||||
| 15 | 1379.104 | -603.104 | ||||||
| 16 | 358.7258 | -209.726 | ||||||
| 17 | 2181.151 | -763.151 | ||||||
| 18 | 240.3172 | -33.3172 | ||||||
| 19 | 2186.522 | -778.522 | ||||||
| 20 | 809.8647 | 853.1353 |
Outliers
From the result of the P-value, we can see that the model did not have any outliers ( absence of outliers). This is because all of the variables have a reasonable p-value
The highest variable p-value was the “2017 NAICS” at .876785 , the value isn’t enough reason to regard this variable as an outlier.
| SUMMARY OUTPUT | |||||||||
| Regression Statistics | |||||||||
| Multiple R | 0.989512 | ||||||||
| R Square | 0.979134 | ||||||||
| Adjusted R Square | 0.97357 | ||||||||
| Standard Error | 560.3778 | ||||||||
| Observations | 20 | ||||||||
| ANOVA | |||||||||
| df | SS | MS | F | Significance F | |||||
| Regression | 4 | 2.21E+08 | 55258993 | 175.971 | 2.08E-12 | ||||
| Residual | 15 | 4710349 | 314023.3 | ||||||
| Total | 19 | 2.26E+08 | |||||||
| Coefficients | Standard Error | t Stat | P-value | Lower 95% | Upper 95% | Lower 95.0% | Upper 95.0% | ||
| Intercept | 80.18125 | 402.4224 | 0.199247 | 0.844746 | -777.562 | 937.9242 | -777.562 | 937.9242 | |
| Emplyment | 0.071086 | 0.019462 | 3.65246 | 0.002358 | 0.029602 | 0.112569 | 0.029602 | 0.112569 | |
| 1st Quarter payroll | -0.0062 | 0.01697 | -0.36561 | 0.719757 | -0.04237 | 0.029966 | -0.04237 | 0.029966 | |
| Annual Payroll | 0.001318 | 0.004199 | 0.313769 | 0.758017 | -0.00763 | 0.010268 | -0.00763 | 0.010268 | |
| 2017 NAICS | -1.18884 | 7.537925 | -0.15771 | 0.876785 | -17.2555 | 14.87787 | -17.2555 | 14.87787 | |
| RESIDUAL OUTPUT | |||||||||
| Observation | Predicted Y | Residuals | |||||||
| 1 | 15732.2 | 188.803 | |||||||
| 2 | 140.6094 | 1.390577 | |||||||
| 3 | 80.72567 | -46.7257 | |||||||
| 4 | 81.94295 | -25.9429 | |||||||
| 5 | 1133.269 | 233.7314 | |||||||
| 6 | 1556.223 | -988.223 | |||||||
| 7 | 646.3199 | 210.6801 | |||||||
| 8 | 2484.405 | 326.5951 | |||||||
| 9 | 655.5826 | -81.5826 | |||||||
| 10 | 256.1365 | 27.86351 | |||||||
| 11 | 591.6482 | 592.3518 | |||||||
| 12 | 313.033 | 553.967 | |||||||
| 13 | 741.3139 | 690.6861 | |||||||
| 14 | 253.91 | -148.91 | |||||||
| 15 | 1379.104 | -603.104 | |||||||
| 16 | 358.7258 | -209.726 | |||||||
| 17 | 2181.151 | -763.151 | |||||||
| 18 | 240.3172 | -33.3172 | |||||||
| 19 | 2186.522 | -778.522 | |||||||
| 20 | 809.8647 | 853.1353 |
New model with only significant variables
The "States” variable was not used because it is non-numerical.
Non-significant variables that were removed.
New model
| State FIPS | State | 116th Congressional District | Number of Establishments | Employment | 1st Quarter Payroll ($1,000) | Annual Payroll ($1,000) | 2017 NAICS Code |
| 01 | Alabama | 01 | 15,921 | 244,615 | 2,492,282 | 10,417,508 | 0.00 |
| 01 | Alabama | 01 | 142 | 1,127 | 10,591 | 44,855 | 11.00 |
| 01 | Alabama | 01 | 34 | 500 | 10,491 | 41,785 | 21.00 |
| 01 | Alabama | 01 | 56 | 1,618 | 46,260 | 151,722 | 22.00 |
| 01 | Alabama | 01 | 1,367 | 16,277 | 194,035 | 855,500 | 23.00 |
| 01 | Alabama | 01 | 568 | 27,761 | 477,179 | 1,897,405 | 31.00 |
| 01 | Alabama | 01 | 857 | 10,723 | 152,635 | 607,774 | 42.00 |
| 01 | Alabama | 01 | 2,811 | 37,463 | 248,940 | 1,015,434 | 44.00 |
| 01 | Alabama | 01 | 574 | 9,862 | 114,653 | 487,821 | 48.00 |
| 01 | Alabama | 01 | 284 | 4,229 | 64,288 | 254,116 | 51.00 |
| 01 | Alabama | 01 | 1,184 | 9,273 | 139,135 | 589,963 | 52.00 |
| 01 | Alabama | 01 | 867 | 4,411 | 39,547 | 172,784 | 53.00 |
| 01 | Alabama | 01 | 1,432 | 12,406 | 201,202 | 828,587 | 54.00 |
| 01 | Alabama | 01 | 105 | 3,216 | 67,676 | 326,639 | 55.00 |
| 01 | Alabama | 01 | 776 | 20,049 | 142,193 | 624,241 | 56.00 |
| 01 | Alabama | 01 | 149 | 5,247 | 35,641 | 151,186 | 61.00 |
| 01 | Alabama | 01 | 1,418 | 32,773 | 336,896 | 1,468,707 | 62.00 |
| 01 | Alabama | 01 | 207 | 3,514 | 12,609 | 55,387 | 71.00 |
| 01 | Alabama | 01 | 1,408 | 31,656 | 122,659 | 533,285 | 72.00 |
| 01 | Alabama | 01 | 1,663 | 12,472 | 75,566 | 309,828 | 81.00 |
Non-significant variables that were removed.
Running the model with significant levels only
Alpha= 0.05
R= .99
Adjusted R squared= .98
98% of the variance is explained
with this model
P-value= 1.74E-16
From this "Employment” has the best significant level (1.74E-16) based on the model.
| SUMMARY OUTPUT | ||||||||
| Regression Statistics | ||||||||
| Multiple R | 0.989261 | |||||||
| R Square | 0.978637 | |||||||
| Adjusted R Square | 0.977451 | |||||||
| Standard Error | 517.6088 | |||||||
| Observations | 20 | |||||||
| ANOVA | ||||||||
| df | SS | MS | F | Significance F | ||||
| Regression | 1 | 2.21E+08 | 2.21E+08 | 824.5923 | 1.74E-16 | |||
| Residual | 18 | 4822539 | 267918.8 | |||||
| Total | 19 | 2.26E+08 | ||||||
| Coefficients | Standard Error | t Stat | P-value | Lower 95% | Upper 95% | Lower 95.0% | Upper 95.0% | |
| Intercept | 19.18188 | 128.0339 | 0.149819 | 0.882574 | -249.807 | 288.1711 | -249.807 | 288.1711 |
| X Variable 1 | 0.064268 | 0.002238 | 28.71571 | 1.74E-16 | 0.059566 | 0.06897 | 0.059566 | 0.06897 |
| RESIDUAL OUTPUT | ||||||||
| Observation | Predicted Y | Residuals | ||||||
| 1 | 15740.08 | 180.9158 | ||||||
| 2 | 91.61185 | 50.38815 | ||||||
| 3 | 51.31585 | -17.3159 | ||||||
| 4 | 123.1674 | -67.1674 | ||||||
| 5 | 1065.271 | 301.7289 | ||||||
| 6 | 1803.324 | -1235.32 | ||||||
| 7 | 708.327 | 148.673 | ||||||
| 8 | 2426.852 | 384.1483 | ||||||
| 9 | 652.9923 | -78.9923 | ||||||
| 10 | 290.971 | -6.971 | ||||||
| 11 | 615.1385 | 568.8615 | ||||||
| 12 | 302.6678 | 564.3322 | ||||||
| 13 | 816.49 | 615.51 | ||||||
| 14 | 225.8676 | -120.868 | ||||||
| 15 | 1307.69 | -531.69 | ||||||
| 16 | 356.3958 | -207.396 | ||||||
| 17 | 2125.435 | -707.435 | ||||||
| 18 | 245.0194 | -38.0194 | ||||||
| 19 | 2053.648 | -645.648 | ||||||
| 20 | 820.7316 | 842.2684 |
Results of new model using only significant variables.
“Employment” started at a p-value of 0.00236 and now it carries a p-value of a value so small we consider it 1.74E-16 . Making it the most significant variable
Adjusted R squared = 0.977451 this number slightly increased from original Adjusted R squared which was 0.97357. indicating that 98% of the variance can be explained by this model.
| SUMMARY OUTPUT | ||||||||
| Regression Statistics | ||||||||
| Multiple R | 0.989261 | |||||||
| R Square | 0.978637 | |||||||
| Adjusted R Square | 0.977451 | |||||||
| Standard Error | 517.6088 | |||||||
| Observations | 20 | |||||||
| ANOVA | ||||||||
| df | SS | MS | F | Significance F | ||||
| Regression | 1 | 2.21E+08 | 2.21E+08 | 824.5923 | 1.74E-16 | |||
| Residual | 18 | 4822539 | 267918.8 | |||||
| Total | 19 | 2.26E+08 | ||||||
| Coefficients | Standard Error | t Stat | P-value | Lower 95% | Upper 95% | Lower 95.0% | Upper 95.0% | |
| Intercept | 19.18188 | 128.0339 | 0.149819 | 0.882574 | -249.807 | 288.1711 | -249.807 | 288.1711 |
| X Variable 1 | 0.064268 | 0.002238 | 28.71571 | 1.74E-16 | 0.059566 | 0.06897 | 0.059566 | 0.06897 |
| RESIDUAL OUTPUT | ||||||||
| Observation | Predicted Y | Residuals | ||||||
| 1 | 15740.08 | 180.9158 | ||||||
| 2 | 91.61185 | 50.38815 | ||||||
| 3 | 51.31585 | -17.3159 | ||||||
| 4 | 123.1674 | -67.1674 | ||||||
| 5 | 1065.271 | 301.7289 | ||||||
| 6 | 1803.324 | -1235.32 | ||||||
| 7 | 708.327 | 148.673 | ||||||
| 8 | 2426.852 | 384.1483 | ||||||
| 9 | 652.9923 | -78.9923 | ||||||
| 10 | 290.971 | -6.971 | ||||||
| 11 | 615.1385 | 568.8615 | ||||||
| 12 | 302.6678 | 564.3322 | ||||||
| 13 | 816.49 | 615.51 | ||||||
| 14 | 225.8676 | -120.868 | ||||||
| 15 | 1307.69 | -531.69 | ||||||
| 16 | 356.3958 | -207.396 | ||||||
| 17 | 2125.435 | -707.435 | ||||||
| 18 | 245.0194 | -38.0194 | ||||||
| 19 | 2053.648 | -645.648 | ||||||
| 20 | 820.7316 | 842.2684 |
Coefficients of new model
For every change in the X variable (independent variables), the Y variable (dependent variable) will change as well.
For Employment variable, the coefficient is 0.06427.
In this case therefore, employment increases number of establishment by 6.43 %.
| SUMMARY OUTPUT | |||||||||
| Regression Statistics | |||||||||
| Multiple R | 0.989261 | ||||||||
| R Square | 0.978637 | ||||||||
| Adjusted R Square | 0.977451 | ||||||||
| Standard Error | 517.6088 | ||||||||
| Observations | 20 | ||||||||
| ANOVA | |||||||||
| df | SS | MS | F | Significance F | |||||
| Regression | 1 | 2.21E+08 | 2.21E+08 | 824.5923 | 1.74E-16 | ||||
| Residual | 18 | 4822539 | 267918.8 | ||||||
| Total | 19 | 2.26E+08 | |||||||
| Coefficients | Standard Error | t Stat | P-value | Lower 95% | Upper 95% | Lower 95.0% | Upper 95.0% | ||
| Intercept | 19.18188 | 128.0339 | 0.149819 | 0.882574 | -249.807 | 288.1711 | -249.807 | 288.1711 | |
| X Variable 1 | 0.064268 | 0.002238 | 28.71571 | 1.74E-16 | 0.059566 | 0.06897 | 0.059566 | 0.06897 | |
| RESIDUAL OUTPUT | |||||||||
| Observation | Predicted Y | Residuals | |||||||
| 1 | 15740.08 | 180.9158 | |||||||
| 2 | 91.61185 | 50.38815 | |||||||
| 3 | 51.31585 | -17.3159 | |||||||
| 4 | 123.1674 | -67.1674 | |||||||
| 5 | 1065.271 | 301.7289 | |||||||
| 6 | 1803.324 | -1235.32 | |||||||
| 7 | 708.327 | 148.673 | |||||||
| 8 | 2426.852 | 384.1483 | |||||||
| 9 | 652.9923 | -78.9923 | |||||||
| 10 | 290.971 | -6.971 | |||||||
| 11 | 615.1385 | 568.8615 | |||||||
| 12 | 302.6678 | 564.3322 | |||||||
| 13 | 816.49 | 615.51 | |||||||
| 14 | 225.8676 | -120.868 | |||||||
| 15 | 1307.69 | -531.69 | |||||||
| 16 | 356.3958 | -207.396 | |||||||
| 17 | 2125.435 | -707.435 | |||||||
| 18 | 245.0194 | -38.0194 | |||||||
| 19 | 2053.648 | -645.648 | |||||||
| 20 | 820.7316 | 842.2684 |
Predictions
The original data was out of 72 states. However, only one state was used.
Predictions will be based on the significant variables
State used: Alabama state
Predictions
It is clear that employment influences the number of establishment
Y=19.18188+ 0.064268 X
(Number of Establishment)=19.18188+ 0.064268(Employment)
Therefore, as employment increases, the number of establishment also increases.
dependent variable
categorical with 1 level
independent variables
Binary variables
Sheet1
| Top 100 Private Colleges | |||||||||||||||||
| Quality Measures | Financial Measures | ||||||||||||||||
| Overall Rank | School | State | Undergrad. Enrollment | Admission Rate | *SAT or ACT | Student/faculty Ratio | 4-year Grad. Rate | 6-year Grad. Rate | Quality Rank | Total Costs | Cost After Need-based Aid | Need Met | Aid From Grants | Cost After Non-Need-Based Aid | Non-Need-Based Aid+ | Average Debt | Cost Rank |
| 1 | California Institute of Technology | CA | 939 | 21% | 99/100% | 3 | 71% | 85% | 10 | $32,682 | $10,981 | 100% | 93% | $18,553 | 15% | $10,244 | 4 |
| 2 | Rice University | TX | 2,787 | 24% | 89/92% | 5 | 68% | 89% | 19 | $28,350 | $14,779 | 100% | 88% | $22,418 | 34% | $12,705 | 5 |
| 3 | Williams College | MA | 1,985 | 23% | 93/93% | 8 | 89% | 94% | 1 | $36,550 | $14,737 | 100% | 89% | $33,251 | NA | $12,316 | 26 |
| 4 | Swarthmore College | PA | 1,479 | 24% | 94/98% | 8 | 86% | 92% | 4 | $38,676 | $17,386 | 100% | 85% | $11,404 | 2% | $12,759 | 21 |
| 5 | Amherst College | MA | 1,618 | 18% | 94/92% | 9 | 84% | 94% | 5 | $38,492 | $14,453 | 100% | 92% | $33,411 | NA | $11,544 | 38 |
| 6 | Webb Institute | NY | 67 | 42% | 100/100% | 7 | 79% | 83% | 39 | $8,079 | $5,579 | 20% | 100% | $8,079 | 100% | $5,700 | 1 |
| 7 | Yale University | CT | 5,339 | 8% | 96/97% | 7 | 88% | 95% | 3 | $38,432 | $15,729 | 100% | 89% | $38,432 | NA | $19,228 | 53 |
| 8 | Washington and Lee University | VA | 1,750 | 31% | 89/89% | 11 | 86% | 89% | 30 | $30,225 | $15,452 | 99% | 87% | $22,063 | 31% | $15,634 | 9 |
| 9 | Harvard University | MA | 6,637 | 11% | 90*/90*% | 8 | 86% | 97% | 8 | $38,831 | $17,456 | 100% | 90% | $33,201 | NA | $10,465 | 46 |
| 10 | Stanford University | CA | 7,360 | 13% | 93/95% | 7 | 77% | 93% | 6 | $38,875 | $17,746 | 100% | 86% | $33,709 | NA | $15,782 | 62 |
| 11 | Princeton University | NJ | 4,779 | 11% | 95/97% | 5 | 91% | 97% | 7 | $40,169 | $18,325 | 100% | 94% | $40,169 | NA | $12,000 | 59 |
| 12 | Massachusetts Institute of Technology | MA | 4,178 | 16% | 95/100% | 6 | 82% | 91% | 2 | $39,213 | $19,609 | 100% | 85% | $30,337 | NA | $22,855 | 82 |
| 13 | Pomona College | CA | 1,551 | 23% | 98/97% | 9 | 83% | 88% | 21 | $38,130 | $17,411 | 100% | 80% | $35,702 | NA | $15,600 | 43 |
| 14 | Emory University | GA | 6,302 | 42% | 89/94% | 7 | 82% | 87% | 15 | $37,272 | $19,657 | 100% | 73% | $23,615 | 19% | $17,675 | 54 |
| 15 | Columbia University | NY | 4,109 | 12% | 91/93% | 7 | 83% | 93% | 13 | $39,493 | $17,778 | 100% | 86% | $39,493 | NA | $15,331 | 65 |
| 16 | Duke University | NC | 6,206 | 25% | 91/94% | 11 | 88% | 93% | 11 | $40,080 | $19,996 | 100% | 80% | $26,599 | 6% | $20,025 | 68 |
| 17 | Davidson College | NC | 1,645 | 34% | 86/89% | 10 | 89% | 91% | 27 | $34,706 | $21,455 | 100% | 82% | $28,630 | 35% | $13,697 | 37 |
| 18 | Wellesley College | MA | 2,300 | 47% | 88/89% | 9 | 84% | 88% | 32 | $37,419 | $17,526 | 100% | 88% | $32,919 | NA | $15,697 | 35 |
| 19 | Vassar College | NY | 2,472 | 31% | 93/89% | 9 | 81% | 87% | 22 | $37,870 | $19,404 | 100% | 78% | $34,669 | NA | $17,170 | 64 |
| 20 | Haverford College | PA | 1,105 | 32% | 89/90% | 8 | 89% | 92% | 20 | $38,928 | $17,826 | 100% | 90% | $38,928 | NA | $15,253 | 66 |
| 21 | Northwestern University | IL | 7,946 | 33% | 88/92% | 7 | 83% | 92% | 17 | $38,817 | $20,376 | 100% | 79% | $36,538 | 12% | $14,551 | 74 |
| 22 | Bowdoin College | ME | 1,657 | 25% | 87/92% | 10 | 83% | 90% | 25 | $38,663 | $17,773 | 100% | 85% | $37,663 | 4% | $15,307 | 58 |
| 23 | University of Pennsylvania | PA | 9,742 | 21% | 91/96% | 6 | 83% | 91% | 9 | $39,040 | $20,596 | 100% | 77% | $39,040 | NA | $20,247 | 93 |
| 24 | Johns Hopkins University | MD | 4,112 | 35% | 85/93% | 8 | 81% | 88% | 29 | $39,188 | $19,142 | 95% | 80% | $24,206 | 9% | $13,600 | 48 |
| 25 | Cooper Union | NY | 917 | 14% | 81/83% | 7 | 57% | 78% | 61 | $14,652 | $11,167 | 92% | 62% | $14,653 | 100% | $9,250 | 3 |
| 26 | Washington University | MO | 7,219 | 24% | 93/98% | 7 | 75% | 86% | 16 | $39,253 | $20,700 | 100% | 81% | $30,581 | 19% | $0 | 87 |
| 27 | Dartmouth College | NH | 4,118 | 23% | 92/96% | 9 | 87% | 95% | 12 | $38,898 | $19,546 | 100% | 76% | $36,482 | NA | $0 | 92 |
| 28 | Claremont McKenna College | CA | 1,024 | 28% | 89/95% | 7 | 82% | 86% | 37 | $37,730 | $17,988 | 100% | 86% | $31,570 | 24% | $16,914 | 41 |
| 29 | University of Notre Dame | IN | 8,261 | 34% | 83/91% | 12 | 88% | 95% | 36 | $35,392 | $18,011 | 100% | 74% | $26,304 | 5% | $25,595 | 45 |
| 30 | Colgate University | NY | 2,827 | 34% | 80/86% | 10 | 85% | 89% | 31 | $38,820 | $18,856 | 100% | 85% | $38,820 | NA | $12,984 | 67 |
| 31 | The Colorado College | CO | 1,902 | 53% | 66/70% | 9 | 72% | 79% | 57 | $35,275 | $16,516 | 95% | 88% | $19,645 | 23% | $13,500 | 10 |
| 32 | University of Richmond | VA | 2,998 | 41% | 74/83% | 10 | 79% | 84% | 48 | $31,679 | $17,588 | 96% | 80% | $21,227 | 40% | $16,115 | 12 |
| 33 | Georgetown University | DC | 6,332 | 21% | 87/89% | 11 | 86% | 91% | 14 | $39,182 | $24,382 | 100% | 68% | $32,832 | NA | $20,000 | 97 |
| 34 | Brown University | RI | 6,030 | 17% | 86/90% | 8 | 79% | 94% | 23 | $40,248 | $20,838 | 100% | 83% | $37,243 | NA | $21,700 | 91 |
| 35 | Carleton College | MN | 1,932 | 35% | 88/89% | 9 | 82% | 86% | 34 | $35,288 | $21,677 | 100% | 72% | $32,968 | 17% | $14,543 | 56 |
| 36 | Lafayette College | PA | 2,300 | 36% | 63/78% | 11 | 79% | 84% | 47 | $35,713 | $15,147 | 94% | 100% | $25,050 | 17% | $17,380 | 19 |
| 37 | Middlebury College | VT | 2,297 | 27% | 93/96% | 11 | 81% | 87% | 18 | $39,532 | $18,288 | 100% | 79% | $39,532 | NA | $21,751 | 98 |
| 38 | Grinnell College | IA | 1,485 | 65% | 87/85% | 10 | 78% | 84% | 55 | $31,460 | $16,585 | 100% | 76% | $23,312 | 65% | $13,854 | 17 |
| 39 | Illinois Wesleyan University | IL | 2,107 | 48% | 96% | 12 | 76% | 81% | 44 | $30,780 | $18,858 | 95% | 72% | $23,095 | 76% | $17,722 | 27 |
| 40 | Bates College | ME | 1,738 | 28% | 90/91% | 10 | 82% | 87% | 28 | $38,932 | $18,258 | 100% | 85% | $38,932 | NA | $17,045 | 88 |
| 41 | Cornell University | NY | 13,725 | 29% | 85/92% | 9 | 82% | 90% | 26 | $38,974 | $23,122 | 100% | 69% | $38,974 | NA | $15,587 | 95 |
| 42 | Wesleyan University | CT | 2,733 | 28% | 89/92% | 9 | 76% | 81% | 24 | $39,127 | $21,401 | 100% | 72% | $39,127 | NA | $23,753 | 99 |
| 43 | Colby College | ME | 1,830 | 33% | 84/89% | 11 | 85% | 88% | 33 | $38,699 | $18,168 | 100% | 93% | $38,699 | NA | $17,270 | 84 |
| 44 | Bucknell University | PA | 3,440 | 39% | 72/84% | 12 | 83% | 87% | 43 | $36,165 | $19,165 | 100% | 94% | $36,165 | NA | $16,000 | 44 |
| 45 | Kenyon College | OH | 1,576 | 52% | 87/81% | 9 | 80% | 84% | 51 | $36,273 | $17,905 | 98% | 85% | $25,183 | 39% | $20,850 | 32 |
| 46 | Centre College | KY | 1,055 | 78% | 89% | 11 | 71% | 73% | 68 | $28,529 | $15,842 | 100% | 65% | $19,002 | 23% | $14,300 | 11 |
| 47 | Rhodes College | TN | 1,541 | 70% | 95% | 11 | 71% | 73% | 64 | $30,080 | $18,899 | 84% | 70% | $21,296 | 50% | $15,100 | 15 |
| 48 | Macalester College | MN | 1,840 | 44% | 87/88% | 10 | 71% | 77% | 58 | $32,847 | $16,394 | 100% | 80% | $27,419 | 26% | $0 | 29 |
| 49 | Barnard College | NY | 2,297 | 34% | 88/88% | 10 | 72% | 84% | 46 | $37,940 | $17,826 | 100% | 82% | $33,701 | 8% | $14,030 | 42 |
| 50 | Brandeis University | MA | 3,057 | 42% | 88/88% | 8 | 79% | 85% | 38 | $39,101 | $22,257 | 84% | 80% | $24,255 | 42% | $0 | 81 |
| 51 | College of the Holy Cross | MA | 2,801 | 43% | 71/76% | 11 | 88% | 90% | 41 | $36,851 | $23,846 | 100% | 71% | $28,381 | 15% | $16,063 | 69 |
| 52 | Harvey Mudd College | CA | 699 | 37% | 97/100% | 9 | 75% | 83% | 35 | $38,880 | $22,041 | 100% | 79% | $32,890 | 58% | $20,219 | 90 |
| 53 | Wake Forest University | NC | 4,045 | 41% | 79/86% | 10 | 77% | 87% | 42 | $36,079 | $21,196 | 90% | 77% | $27,438 | 45% | $24,769 | 61 |
| 54 | Bryn Mawr College | PA | 1,321 | 50% | 86/75% | 9 | 76% | 80% | 45 | $37,890 | $18,609 | 96% | 86% | $36,160 | NA | $0 | 57 |
| 54 | Wheaton College | IL | 2,395 | 54% | 84/83% | 11 | 70% | 84% | 66 | $27,076 | $17,341 | 97% | 74% | $22,678 | 11% | $15,864 | 24 |
| 55 | Tufts University | MA | 4,910 | 27% | 81/90% | 9 | 81% | 88% | 40 | $39,173 | $20,115 | 100% | 85% | $37,477 | 4% | $15,499 | 79 |
| 56 | Oberlin College | OH | 2,848 | 33% | 87/80% | 10 | 63% | 76% | 50 | $37,688 | $21,081 | 100% | 72% | $26,683 | 26% | $13,926 | 50 |
| 57 | Mount Holyoke College | MA | 2,191 | 52% | 80/70% | 10 | 75% | 79% | 49 | $38,668 | $19,268 | 100% | 76% | $28,368 | 10% | $14,200 | 51 |
| 58 | Furman University | SC | 2,772 | 58% | 65/70% | 11 | 74% | 81% | 69 | $29,430 | $16,296 | 90% | 72% | $20,230 | 55% | $17,741 | 14 |
| 59 | St. Olaf College | MN | 3,041 | 73% | 84% | 13 | 71% | 75% | 67 | $29,879 | $17,458 | 100% | 74% | $25,254 | 48% | $18,806 | 25 |
| 60 | Brigham Young University | UT | 29,379 | 73% | 86% | 18 | 31% | 73% | 95 | $9,663 | $7,621 | 40% | 53% | $6,523 | 38% | $11,000 | 2 |
| 61 | Lehigh University | PA | 4,706 | 44% | 59/85% | 11 | 70% | 84% | 65 | $35,670 | $19,123 | 99% | 75% | $23,231 | 14% | $16,972 | 30 |
| 62 | Smith College | MA | 2,647 | 53% | 72/66% | 9 | 76% | 80% | 56 | $37,937 | $18,466 | 100% | 76% | $28,306 | 11% | $19,911 | 52 |
| 63 | Beloit College | WI | 1,281 | 70% | 82% | 11 | 60% | 72% | 70 | $30,264 | $17,452 | 100% | 72% | $23,690 | 19% | $14,942 | 24 |
| 64 | Taylor University | IN | 1,869 | 78% | 74% | 15 | 71% | 75% | 90 | $24,723 | $15,678 | 81% | 73% | $20,538 | 60% | $15,117 | 7 |
| 65 | Union College | NY | 2,147 | 45% | 56/71% | 11 | 75% | 80% | 72 | $36,455 | $18,431 | 97% | 79% | $16,455 | 1% | $15,725 | 22 |
| 66 | Hamilton College | NY | 1,851 | 35% | 77/82% | 10 | 79% | 84% | 54 | $38,463 | $19,474 | 99% | 85% | $29,638 | 8% | $16,856 | 55 |
| 67 | DePauw University | IN | 2,338 | 61% | 55/60% | 11 | 75% | 79% | 88 | $32,150 | $15,531 | 99% | 82% | $21,813 | 81% | $14,481 | 8 |
| 68 | Hillsdale College | MI | 1,220 | 82% | 74% | 11 | 53% | 71% | 99 | $23,353 | $13,853 | 77% | 68% | $16,853 | 45% | $14,500 | 6 |
| 69 | Knox College | IL | 1,121 | 72% | 72% | 12 | 67% | 74% | 80 | $30,894 | $15,494 | 99% | 76% | $21,205 | 67% | $16,920 | 13 |
| 70 | University of Southern California | CA | 16,145 | 30% | 79/91% | 10 | 51% | 73% | 59 | $37,968 | $21,606 | 99% | 68% | $25,660 | 25% | $20,619 | 70 |
| 71 | Trinity College | CT | 2,098 | 36% | 73/79% | 9 | 77% | 83% | 53 | $38,890 | $19,667 | 100% | 85% | $33,390 | 1% | $17,000 | 78 |
| 72 | Trinity University | TX | 2,406 | 69% | 71/80% | 11 | 65% | 75% | 86 | $27,086 | $16,706 | 86% | 71% | $21,193 | 54% | $0 | 20 |
| 73 | Gustavus Adolphus College | MN | 2,536 | 77% | 70% | 13 | 72% | 75% | 89 | $27,820 | $17,609 | 92% | 70% | $21,977 | 82% | $17,400 | 18 |
| 74 | Vanderbilt University | TN | 6,146 | 46% | 83/90% | 9 | 78% | 84% | 52 | $38,847 | $20,971 | 99% | 64% | $23,049 | 27% | $24,023 | 86 |
| 75 | Whitman College | WA | 1,454 | 50% | 80/81% | 10 | 60% | 71% | 74 | $33,776 | $21,176 | 94% | 70% | $25,776 | 72% | $15,000 | 36 |
| 76 | Scripps College | CA | 798 | 58% | 85/78% | 12 | 63% | 68% | 91 | $36,500 | $17,984 | 100% | 78% | $21,355 | 13% | $12,941 | 23 |
| 77 | Franklin and Marshall College | PA | 1,926 | 62% | 62/71% | 11 | 78% | 83% | 73 | $36,580 | $20,925 | 98% | 80% | $24,751 | 33% | $19,656 | 40 |
| 78 | Saint Louis University | MO | 7,178 | 72% | 72% | 12 | 52% | 67% | 100 | $29,983 | $16,902 | 71% | 63% | $21,714 | 36% | $14,989 | 16 |
| 79 | Carnegie Mellon University | PA | 5,475 | 38% | 75/95% | 11 | 61% | 77% | 63 | $38,460 | $24,689 | 83% | 70% | $25,952 | 22% | $19,195 | 76 |
| 80 | Lawrence University | WI | 1,389 | 68% | 83% | 11 | 58% | 68% | 83 | $32,875 | $17,882 | 100% | 74% | $25,093 | 65% | $18,311 | 34 |
| 81 | Connecticut College | CT | 1,890 | 35% | 83/84% | 11 | 75% | 81% | 62 | $37,057 | $16,930 | 100% | 86% | $37,057 | NA | $17,250 | 85 |
| 82 | Case Western Reserve University | OH | 3,457 | 78% | 74/85% | 8 | 49% | 75% | 87 | $32,802 | $18,323 | 96% | 66% | $20,907 | 66% | $21,830 | 31 |
| 84 | Dickinson College | PA | 2,261 | 51% | 65/64% | 13 | 74% | 78% | 79 | $36,600 | $19,753 | 98% | 76% | $24,515 | 30% | $17,586 | 39 |
| 85 | Kalamazoo College | MI | 1,265 | 73% | 91% | 12 | 60% | 69% | 92 | $30,917 | $17,947 | NA% | 68% | $21,467 | 92% | $20,000 | 33 |
| 86 | Saint John's University | MN | 1,897 | 87% | 66% | 13 | 67% | 74% | 97 | $27,272 | $19,544 | 88% | 46% | $21,687 | 68% | $20,680 | 28 |
| 87 | Boston College | MA | 9,000 | 34% | 78/85% | 13 | 0% | 86% | 71 | $37,745 | $24,470 | 100% | 70% | $32,160 | 7% | $16,732 | 73 |
| 88 | Reed College | OR | 1,363 | 55% | 95/86% | 10 | 45% | 67% | 85 | $37,900 | $18,804 | 100% | 90% | $37,900 | NA | $16,758 | 47 |
| 89 | Bard College | NY | 1,454 | 36% | 85/67% | 9 | 59% | 71% | 82 | $38,282 | $20,558 | 87% | 83% | $23,338 | 11% | $15,400 | 49 |
| 90 | University of Rochester | NY | 4,695 | 50% | 79/87% | 12 | 65% | 76% | 76 | $37,246 | $20,297 | 100% | 78% | $27,245 | 53% | $0 | 60 |
| 91 | New York University | NY | 19,490 | 28% | 87/86% | 11 | 65% | 74% | 60 | $40,105 | $28,282 | 70% | 67% | $33,355 | 26% | $21,495 | 100 |
| 92 | Villanova University | PA | 7,375 | 47% | 57/74% | 13 | 79% | 84% | 75 | $36,560 | $26,463 | 76% | 57% | $29,161 | 20% | $28,217 | 72 |
| 93 | Skidmore College | NY | 2,506 | 46% | 70/69% | 11 | 71% | 75% | 78 | $38,838 | $21,023 | 98% | 77% | $29,438 | 1% | $15,560 | 71 |
| 94 | Rose-Hulman Institute of Technology | IN | 1,642 | 65% | 62/91% | 13 | 58% | 71% | 93 | $32,625 | $28,677 | 60% | 27% | $28,720 | 65% | $27,000 | 63 |
| 95 | St. John's College | MD | 465 | 71% | 95/75% | 8 | 63% | 71% | 81 | $36,635 | $21,940 | 91% | 72% | $34,477 | 4% | $20,753 | 75 |
| 96 | Babson College | MA | 1,735 | 48% | 50/77% | 13 | 77% | 81% | 77 | $38,443 | $21,316 | 98% | 78% | $30,308 | 11% | $0 | 83 |
| 97 | Rhode Island School of Design | RI | 1,882 | 32% | 49/55% | 11 | 0% | 87% | 96 | $34,472 | $26,447 | 69% | 53% | $33,222 | 4% | $21,125 | 80 |
| 98 | Rensselaer Polytechnic Institute | NY | 5,139 | 70% | 68/92% | 17 | 48% | 75% | 84 | $39,200 | $22,360 | 90% | 74% | $28,411 | 45% | $24,590 | 94 |
| 99 | Sarah Lawrence College | NY | 1,226 | 40% | 79/44% | 6 | 51% | 66% | 94 | $42,121 | $22,847 | 94% | 73% | $33,610 | NA | $14,864 | 89 |
| 100 | The George Washington University | DC | 10,328 | 40% | 68/72% | 14 | 62% | 73% | 98 | $40,240 | $25,866 | 94% | 56% | $29,916 | 25% | $0 | 96 |
| *SAT or ACT. Shows the percentage of the 2002-2003 freshman class who scored above 600 on the verbal component of the SAT I and the percentage of those students that scored above 600 on the math component, separated by a slash, or the percentage that scor | |||||||||||||||||
| From Kiplinger: http://www.kiplinger.com/tools/colleges/ |
Sheet2
| 6-year Grad. Rate | State | Student/faculty Ratio | Aid From Grants | West | South East | Undergrad. Enrollment | Republican State | Football team | 4-year Grad. Rate | Total Costs | |
| California Institute of Technology | 0.85 | CA | 3 | 0.93 | 1 | 0 | 939 | 0 | 0 | 0.71 | 32682 |
| Rice University | 0.89 | TX | 5 | 0.88 | 1 | 0 | 2787 | 1 | 1 | 0.68 | 28350 |
| Williams College | 0.94 | MA | 8 | 0.89 | 0 | 0 | 1985 | 0 | 1 | 0.89 | 36550 |
| Swarthmore College | 0.92 | PA | 8 | 0.85 | 0 | 0 | 1479 | 1 | 0 | 0.86 | 38676 |
| Amherst College | 0.94 | MA | 9 | 0.92 | 0 | 0 | 1618 | 0 | 1 | 0.84 | 38492 |
| Webb Institute | 0.83 | NY | 7 | 1 | 0 | 0 | 67 | 1 | 1 | 0.79 | 8079 |
| Yale University | 0.95 | CT | 7 | 0.89 | 0 | 0 | 5339 | 0 | 1 | 0.88 | 38432 |
| Washington and Lee University | 0.89 | VA | 11 | 0.87 | 0 | 1 | 1750 | 1 | 1 | 0.86 | 30225 |
| Harvard University | 0.97 | MA | 8 | 0.9 | 0 | 0 | 6637 | 0 | 1 | 0.86 | 38831 |
| Stanford University | 0.93 | CA | 7 | 0.86 | 1 | 0 | 7360 | 0 | 1 | 0.77 | 38875 |
| Princeton University | 0.97 | NJ | 5 | 0.94 | 0 | 0 | 4779 | 0 | 1 | 0.91 | 40169 |
| Massachusetts Institute of Technology | 0.91 | MA | 6 | 0.85 | 0 | 0 | 4178 | 0 | 1 | 0.82 | 39213 |
| Pomona College | 0.88 | CA | 9 | 0.8 | 1 | 0 | 1551 | 0 | 1 | 0.83 | 38130 |
| Emory University | 0.87 | GA | 7 | 0.73 | 0 | 1 | 6302 | 1 | 0 | 0.82 | 37272 |
| Columbia University | 0.93 | NY | 7 | 0.86 | 0 | 0 | 4109 | 1 | 1 | 0.83 | 39493 |
| Duke University | 0.93 | NC | 11 | 0.8 | 0 | 1 | 6206 | 1 | 1 | 0.88 | 40080 |
| Davidson College | 0.91 | NC | 10 | 0.82 | 0 | 1 | 1645 | 1 | 1 | 0.89 | 34706 |
| Wellesley College | 0.88 | MA | 9 | 0.88 | 0 | 0 | 2300 | 0 | 0 | 0.84 | 37419 |
| Vassar College | 0.87 | NY | 9 | 0.78 | 0 | 0 | 2472 | 1 | 0 | 0.81 | 37870 |
| Haverford College | 0.92 | PA | 8 | 0.9 | 0 | 0 | 1105 | 1 | 0 | 0.89 | 38928 |
| dependent variable | |||||||||||
| categorical with 1 level | |||||||||||
| independent variables | |||||||||||
| Binary variables |
Sheet3
| 6-year Grad. Rate | State | West | South East | Total Costs | Republican State | Football team | Student/faculty Ratio | Undergrad. Enrollment | |
| California Institute of Technology | 0.85 | CA | 1 | 0 | 32682 | 0 | 0 | 3 | 939 |
| Rice University | 0.89 | TX | 1 | 0 | 28350 | 1 | 1 | 5 | 2787 |
| Williams College | 0.94 | MA | 0 | 0 | 36550 | 0 | 1 | 8 | 1985 |
| Swarthmore College | 0.92 | PA | 0 | 0 | 38676 | 1 | 0 | 8 | 1479 |
| Amherst College | 0.94 | MA | 0 | 0 | 38492 | 0 | 1 | 9 | 1618 |
| Webb Institute | 0.83 | NY | 0 | 0 | 8079 | 1 | 1 | 7 | 67 |
| Yale University | 0.95 | CT | 0 | 0 | 38432 | 0 | 1 | 7 | 5339 |
| Washington and Lee University | 0.89 | VA | 0 | 1 | 30225 | 1 | 1 | 11 | 1750 |
| Harvard University | 0.97 | MA | 0 | 0 | 38831 | 0 | 1 | 8 | 6637 |
| Stanford University | 0.93 | CA | 1 | 0 | 38875 | 0 | 1 | 7 | 7360 |
| Princeton University | 0.97 | NJ | 0 | 0 | 40169 | 0 | 1 | 5 | 4779 |
| Massachusetts Institute of Technology | 0.91 | MA | 0 | 0 | 39213 | 0 | 1 | 6 | 4178 |
| Pomona College | 0.88 | CA | 1 | 0 | 38130 | 0 | 1 | 9 | 1551 |
| Emory University | 0.87 | GA | 0 | 1 | 37272 | 1 | 0 | 7 | 6302 |
| Columbia University | 0.93 | NY | 0 | 0 | 39493 | 1 | 1 | 7 | 4109 |
| Duke University | 0.93 | NC | 0 | 1 | 40080 | 1 | 1 | 11 | 6206 |
| Davidson College | 0.91 | NC | 0 | 1 | 34706 | 1 | 1 | 10 | 1645 |
| Wellesley College | 0.88 | MA | 0 | 0 | 37419 | 0 | 0 | 9 | 2300 |
| Vassar College | 0.87 | NY | 0 | 0 | 37870 | 1 | 0 | 9 | 2472 |
| Haverford College | 0.92 | PA | 0 | 0 | 38928 | 1 | 0 | 8 | 1105 |
Sheet4
| SUMMARY OUTPUT | ||||||||
| Regression Statistics | ||||||||
| Multiple R | 0.8985094613 | |||||||
| R Square | 0.807319252 | |||||||
| Adjusted R Square | 0.6949221491 | |||||||
| Standard Error | 0.0211200363 | |||||||
| Observations | 20 | |||||||
| ANOVA | ||||||||
| df | SS | MS | F | Significance F | ||||
| Regression | 7 | 0.0224273288 | 0.0032039041 | 7.1827407529 | 0.001627108 | |||
| Residual | 12 | 0.0053526712 | 0.0004460559 | |||||
| Total | 19 | 0.02778 | ||||||
| Coefficients | Standard Error | t Stat | P-value | Lower 95% | Upper 95% | Lower 95.0% | Upper 95.0% | |
| Intercept | 0.7694264783 | 0.037399937 | 20.5729351692 | 0.0000000001 | 0.6879390158 | 0.8509139407 | 0.6879390158 | 0.8509139407 |
| West | -0.0324817959 | 0.0133721228 | -2.4290680165 | 0.0317866019 | -0.0616171487 | -0.0033464431 | -0.0616171487 | -0.0033464431 |
| South East | -0.0223152775 | 0.0164678937 | -1.3550778203 | 0.20035267 | -0.0581957357 | 0.0135651806 | -0.0581957357 | 0.0135651806 |
| Total Costs | 0.000003492 | 0.0000009221 | 3.7869738942 | 0.0025904833 | 0.0000014829 | 0.0000055011 | 0.0000014829 | 0.0000055011 |
| Republican State | 0.0050589309 | 0.0129398072 | 0.3909587553 | 0.7026802342 | -0.0231344869 | 0.0332523487 | -0.0231344869 | 0.0332523487 |
| Football team | 0.0442552326 | 0.0124103327 | 3.5659988814 | 0.0038808196 | 0.0172154404 | 0.0712950247 | 0.0172154404 | 0.0712950247 |
| Student/faculty Ratio | -0.0018317178 | 0.0033926611 | -0.5399059334 | 0.599138383 | -0.0092236913 | 0.0055602556 | -0.0092236913 | 0.0055602556 |
| Undergrad. Enrollment | 0.0000020839 | 0.0000029468 | 0.7071646151 | 0.4929690742 | -0.0000043366 | 0.0000085044 | -0.0000043366 | 0.0000085044 |
| RESIDUAL OUTPUT | ||||||||
| Observation | Predicted 6-year Grad. Rate | Residuals | ||||||
| 1 | 0.8475315523 | 0.0024684477 | ||||||
| 2 | 0.8819059552 | 0.0080940448 | ||||||
| 3 | 0.9307967388 | 0.0092032612 | ||||||
| 4 | 0.8979699757 | 0.0220300243 | ||||||
| 5 | 0.9349816903 | 0.0050183097 | ||||||
| 6 | 0.8342700371 | -0.0042700371 | ||||||
| 7 | 0.9461896697 | 0.0038103303 | ||||||
| 8 | 0.8854686826 | 0.0045313174 | ||||||
| 9 | 0.9484561139 | 0.0215438861 | ||||||
| 10 | 0.9194663182 | 0.0105336818 | ||||||
| 11 | 0.9547517304 | 0.0152482696 | ||||||
| 12 | 0.9483292653 | -0.0383292653 | ||||||
| 13 | 0.9010961744 | -0.0210961744 | ||||||
| 14 | 0.8826341425 | -0.0126341425 | ||||||
| 15 | 0.9523904494 | -0.0223904494 | ||||||
| 16 | 0.9291679654 | 0.0008320346 | ||||||
| 17 | 0.9027292095 | 0.0072707905 | ||||||
| 18 | 0.8884007468 | -0.0084007468 | ||||||
| 19 | 0.8953929908 | -0.0253929908 | ||||||
| 20 | 0.8980705919 | 0.0219294081 |