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homework_4.docx

QSO 510 Winter 2013

QSO 510 Winter 2013 Homework #4 Page 3

Names: Wiratee Wangthanasakun

Correlation and simple regression

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Question #1:

The Excel file Homework 4 Data.xlsx has a tab labeled “Education income” which provides data on the median income of households in each county in the US and the percentage of the population in each county having a high-school education for the same counties. Plot the data with the high school education on the x-axis and the median income on the y-axis:

Determine the linear regression model of median income versus education using income as the dependent (y) variable. Use the long, SSxx, SSyy, etc. method of calculating the model. Write out the linear equation.

= 76.85704 (Please see excel file)

= 44,839.17 (Please see excel file)

SSxx = 279,175.25 (Please see excel file)

SSyy = 476,875,677,564.75 (Please see excel file)

SSxy = 243,852,830.93 (Please see excel file)

b1 = 873.4758 (Please see excel file)

b0 = -22,293.5969 (Please see excel file)

Linear Equation: y = 873.4758x – 22,293.5969

Determine the correlation coefficient for this relation. Based on the correlation coefficient, do you believe the linear model implies a relation between income and education?

r = 0.67 (Please see excel file)

This coefficient is 0.67 which means there is a relation between high school education and income.

Is it reasonable to expect that income and education are related?

Yes, as we can see from the equation, the slope indicates that the income increases when the percent of high school education increases. And we have the coefficient = 0.67 which is close to 1, thus, we may say that the high school education is one of the factors that indicate the income.

Question #2:

The tab “Education income” also contains the percentage of the population for each county who have a bachelor’s degree. Use the regression tool to calculate a linear model of the income versus a bachelor’s degree (again use income as the dependent variable). Paste the regression report below and write out the linear equation:

Linear Equation: y = 984.0664x + 28,620.5667

What does the p-value or t-statistic for the relation between income and education imply?

The p-value for this relationship is 0. We were using a 95% confidence and if the p-values are under α = 0.05, then there is a statistically meaningful relationship between the two quantities. We may say that more education is more likely to get a higher income.

What is the correlation coefficient? What does it imply about the relation between these two variables? (Note the R2 value is not the correlation coefficient.)

Correlation Coefficient = = 0.6253

It shows a statistically meaningful relationship between bachelor’s degree and median income in my opinion since it’s close to 1.

What do the two models imply about the relative value of a high school or a college education?

Comparing the relationship with the income between having a high school education and having a college education, a high school education seems to have a stronger relationship because its correlation coefficient is a little higher, 0.67 and 0.63 respectively. This is as expected because in order to get a college education, people must have finished a high school degree. In summary, there is a relationship between education and the amount of household income. It tells us that a higher education will give a higher income based on the trending analysis we have done.

High school education(%) vs Median income($)

Income 78.7 82 64.7 63.2 70.400000000000006 60.5 67.8 73.900000000000006 64.2 63.5 66.2 65 70.8 66 62.9 73.2 73.3 67.7 65.7 68.400000000000006 60.1 70.400000000000006 77.8 70.3 63.8 77.599999999999994 68.5 74.099999999999994 66.099999999999994 62.1 65.599999999999994 64.8 65.2 66.7 76.5 67 80.900000000000006 65.099999999999994 76.400000000000006 65.599999999999994 81.400000000000006 74.5 64.3 70 85.4 71.900000000000006 63.2 69.400000000000006 76.7 67.900000000000006 80.3 76.3 62.4 69.7 69.099999999999994 61.9 66.5 71.3 86.8 64.8 69.7 70.099999999999994 78.8 67.2 72.3 59.5 62.6 74.7 78.5 90.3 71 88.9 91.7 76.599999999999994 91.8 88.9 93.2 88.5 89.6 85.4 72.2 88.1 74.8 77.400000000000006 72 84.1 90.6 84.4 86.8 88.5 66.3 85.8 84.3 74.3 63.6 79.5 83.8 78.2 75.599999999999994 82.5 69.3 82.5 77.5 71.2 83.4 72.7 60.7 84.7 65.8 72.400000000000006 72.5 77.5 80.400000000000006 76.8 66.599999999999994 68.7 71.8 64.2 75.3 60.6 74.8 73.099999999999994 74.099999999999994 73.2 77.3 71.5 69.2 68.3 66.8 65 73.099999999999994 83.3 71.099999999999994 72.2 78.3 77.2 72.099999999999994 69.2 73.3 70.7 75.5 73.3 66 74.8 67.599999999999994 65.3 63.3 56.2 65 73.400000000000006 69.8 77.599999999999994 67.8 76 74.3 64.7 63.8 69.8 69.099999999999994 70.2 73.5 73.8 62.2 68.8 62 72.599999999999994 77.400000000000006 68.2 84.4 69.2 65.099999999999994 82.3 65.400000000000006 68 76.599999999999994 64.599999999999994 72.900000000000006 68 74.5 71.599999999999994 79.5 72.900000000000006 60.6 64.099999999999994 82.4 88.3 84 82.3 85.7 64 86.9 71.599999999999994 89.1 67.5 68.5 84.9 59 82.3 68.5 68.8 77.3 79.599999999999994 69.900000000000006 65.400000000000006 91.2 85.1 80.8 63.8 77.099999999999994 87.9 68.400000000000006 80.400000000000006 90.3 79.5 90.5 88 75 83.3 74.900000000000006 74.2 82.6 81.2 71.2 85.6 85.3 79.2 83.4 83.2 83.3 85.2 83.8 83.8 84.9 70.400000000000006 73 75.7 81 61.7 84.3 80.099999999999994 79.8 71.8 78.8 82.6 90.7 87.3 78.5 77.2 92.8 88.5 84.1 93.4 72.099999999999994 68.2 77.5 90.3 80.099999999999994 78.900000000000006 76 97 86.6 92.5 91.3 80.5 85.4 94.1 92.3 94.1 93.1 77.8 86.2 91.8 86.3 77 79.5 91.4 92.3 76.900000000000006 81.8 82.3 85 91.6 79.599999999999994 81.099999999999994 80.7 71.400000000000006 75.7 93.4 93.3 81.599999999999994 96.3 72 81.3 88.4 78.099999999999994 95.3 70 92.1 93.6 79.3 93.3 94 81.7 79.599999999999994 79.5 84.4 82.4 85.9 88.7 83 86 89.2 79.599999999999994 79.400000000000006 85.5 76.5 77.8 88.1 71.900000000000006 81 74.2 86.3 82 69.099999999999994 82.1 78.3 86.4 81.8 74.7 63.5 65.900000000000006 82.7 82.1 85.9 68.3 70.7 72.400000000000006 69.8 72.599999999999994 62.9 58 54.2 78.5 74.5 80.8 65.2 81.599999999999994 69.099999999999994 73.2 68.2 79.8 82.3 89.1 73.900000000000006 65.599999999999994 67.5 81.400000000000006 78.2 85.3 67.900000000000006 84.9 81 88 65.099999999999994 81.8 79.099999999999994 83.6 77.599999999999994 84 74.8 70.400000000000006 87.2 77.7 85.4 87.1 88.7 77.3 73.2 70 72.5 82 78.400000000000006 76 71.2 67.3 56.3 67.7 66 72.599999999999994 65.400000000000006 73.3 71.8 65.8 66 77.2 71.7 72.5 67.5 79 77.900000000000006 64.900000000000006 69.8 65.5 83.3 56.9 71.099999999999994 76 65.099999999999994 80.2 88.8 60.4 84.4 81 64.3 80.099999999999994 58.9 88.8 64.8 64.900000000000006 87.9 64.599999999999994 81.599999999999994 67.3 65.900000000000006 67 79.5 69.7 85.1 66.3 68.5 73.7 81.099999999999994 68.400000000000006 60.5 78.900000000000006 67.2 61.4 65.7 70.900000000000006 92.4 71.5 85.7 67 84 66 66.099999999999994 82.2 65.900000000000006 69.400000000000006 70.099999999999994 87.3 70.900000000000006 70.5 62.2 63 79 71.099999999999994 66 84.2 84.3 67.7 68.099999999999994 69.7 63.3 58.5 62 62.4 77.900000000000006 71.3 67 70.3 81.3 86.8 71 74.3 77.7 72 66.7 71.2 63.2 70.8 65.400000000000006 65.8 69 65.3 77.7 71.400000000000006 74 61.1 78.900000000000006 74.7 86.7 72.099999999999994 80.8 73.400000000000006 70.2 69.8 75.3 63.3 73.400000000000006 75.5 57.8 75.400000000000006 62.4 78 82.4 70 66.900000000000006 67.900000000000006 67.8 71.099999999999994 63.2 69.900000000000006 64.8 56.2 66.3 63.6 63.6 64.5 73.5 67.900000000000006 67.3 75.099999999999994 61.8 73 67.7 63.2 74.2 66.7 66.8 73.5 70.3 57.1 68.3 70.099999999999994 61.3 67.900000000000006 76 63 68.2 65 70.400000000000006 68.3 84.6 84.8 39.5 83.3 83.4 90.8 80.8 87.5 85.5 79.8 80.599999999999994 90.2 86.3 85.6 87.8 80 82.6 88.4 76 86.6 76.900000000000006 64 80.099999999999994 84.5 87.2 88.2 80.400000000000006 79.400000000000006 72.599999999999994 82.9 84.4 75.099999999999994 87.3 91 82.5 84.2 77.400000000000006 88.5 73.7 85.5 86.4 67.599999999999994 74.5 74.7 77.900000000000006 87.3 81.3 88.9 76.599999999999994 83.7 67 72.8 80.8 63.3 84.1 79.900000000000006 83.3 80 91 81 80 75.900000000000006 77.400000000000006 82.9 77.7 79.3 80.2 87.5 83.5 79.3 90 81.400000000000006 82.3 83.4 72.2 86 76.7 78.3 73.599999999999994 78.900000000000006 86.9 74.3 85.7 68.099999999999994 82.4 84.5 80.3 85.2 82.6 77 82.5 83.6 67.099999999999994 80.2 79.8 89.9 81.8 86.6 81.400000000000006 81.3 80.2 78.099999999999994 80.400000000000006 86.9 89.2 90.7 83.2 82.1 84.3 79.099999999999994 85 79.900000000000006 76.5 88.3 84.9 87.2 77.099999999999994 79.900000000000006 78.8 83.1 83.8 72.3 88.7 79.599999999999994 75.8 70.7 83.8 71.3 83.4 82.6 80.900000000000006 76.099999999999994 88.1 83.6 83.1 82.9 83.4 84.1 85 74.8 78.7 82.2 82.3 79.099999999999994 75.2 74.599999999999994 79.8 86.9 79.8 81.400000000000006 87.8 80 85.7 83.8 86.3 81.3 88.3 83.6 83.2 81.8 79.900000000000006 82.3 80.099999999999994 70.599999999999994 71.8 82 79.099999999999994 84.7 81.599999999999994 80.2 75.7 73.7 82.4 80.7 76.099999999999994 80.2 80.900000000000006 79.2 79.2 94.2 87.8 80.3 88.5 79.599999999999994 83.3 85 79.8 82.4 78.5 81 76.2 85.7 81.7 81.599999999999994 60.2 80.7 80.599999999999994 77.400000000000006 80.099999999999994 81.599999999999994 79.8 74.2 81.900000000000006 88.5 85.7 80.7 78.7 77.3 78.400000000000006 73.8 74.900000000000006 80.5 74.8 75.599999999999994 88.3 84.4 79.8 81.2 79.599999999999994 78.900000000000006 79.599999999999994 82.4 71.400000000000006 79.8 81.2 72 84.3 80.8 71.400000000000006 87.8 83.7 79.900000000000006 83.1 81.2 81 81.7 85 86.3 75.2 78.099999999999994 87.3 82.1 86.2 87.8 84.5 81.400000000000006 81.400000000000006 82.5 87.8 86.5 89 87.7 84.6 81.3 82.2 85.4 83.7 85.9 87.7 87.3 87.5 83.4 84.4 88 82.6 85.6 78.5 89.5 78.900000000000006 81.7 85.1 85.8 89.2 85.2 82.2 84.8 85.9 84 85 85.6 86.5 85.4 87.3 85.8 85.7 85 86.1 79.3 86.3 85 87 81.5 86.8 88.1 93.7 85.3 84 85.6 83.6 90.6 79.7 79.099999999999994 78.7 87.6 82.6 84 82.3 83.2 84.4 81.7 82.2 81.8 80.3 80.7 81.099999999999994 85.5 83.7 87.4 86.6 88.3 84 86.7 82.8 84.2 86.3 86.6 80.400000000000006 93.5 84.2 83.3 87.3 82.7 81.5 90 82.5 83.9 84.2 87.3 84.1 81.400000000000006 86 84.4 83.1 81.900000000000006 84.7 85.8 82.3 84.2 84.6 87.3 87.1 81 80.3 85.5 87.4 87 85.5 86.9 91.3 85.4 84.5 86.4 86.4 80.2 92.4 81.2 80 87.2 84.8 67.400000000000006 69.900000000000006 85.3 86 84.5 83.6 71.5 73.599999999999994 83.7 80.900000000000006 76.7 83.8 85.3 74.8 86.9 87.7 88.9 87.6 94.9 75.8 84.7 85.2 83 88.5 86.5 85 80.900000000000006 86.7 81.8 85.9 84.4 85.1 80.3 87.5 88.1 81.2 84.7 81.900000000000006 83.7 83.5 84.4 84.8 85.5 84.8 86.2 84.8 84.4 89.2 86.3 84.7 82.7 88.6 83.4 93.8 87.1 82.8 83.1 87 84.5 85.1 63.7 88.1 87.8 86.6 84.6 82.9 78 80.5 86.3 92.7 84.3 89.9 84 81.2 77.7 81.099999999999994 83.4 74 60.1 64.5 80.400000000000006 76.3 69.5 59 56.6 85.1 75.400000000000006 78 76.599999999999994 69.599999999999994 57.5 68.900000000000006 76 60.7 73.099999999999994 77.900000000000006 80.8 73.400000000000006 68.099999999999994 64.400000000000006 57.4 77.2 75 49.4 53.5 67 56 80.7 61.7 52.6 58.5 85.8 66.5 61.3 78.8 69.5 68 69.400000000000006 72.400000000000006 73.400000000000006 62.8 61.4 75.099999999999994 77.2 82.3 58.7 74.2 58.2 78.3 73.400000000000006 64.400000000000006 71.3 52.9 81.8 79.099999999999994 63.8 82.1 58.7 54.1 71 63.9 58.2 50.9 52.5 58.5 57.4 64.599999999999994 74.3 68.5 68 80.3 52.6 70.8 75.2 50.1 70.5 76.900000000000006 54 73.3 77.900000000000006 57.6 75.8 58 57.8 70.5 56.4 65.8 79 62.9 67 86.5 67.900000000000006 49.2 72.8 58.3 61.8 56.1 65.599999999999994 60.9 57.7 70.900000000000006 61.8 80.5 79.099999999999994 73.599999999999994 75.400000000000006 68 63.5 72.099999999999994 70.7 76.900000000000006 80.3 68.8 57.8 70.900000000000006 61.3 53.6 82.6 64.7 63.2 79.599999999999994 59.4 59.8 75 71.900000000000006 83 78.7 77 65.400000000000006 68.099999999999994 61.4 65.7 64.599999999999994 70.3 83.9 57.9 70.7 55.5 61.4 73.099999999999994 66.900000000000006 65.7 73.599999999999994 79.3 69.400000000000006 79.8 66.3 68.5 80.400000000000006 77.2 63.4 66.599999999999994 72.7 74.7 78.599999999999994 68.7 69.099999999999994 74.599999999999994 67.400000000000006 61.9 70.8 73.099999999999994 80 67.5 73.900000000000006 76.900000000000006 62 62.9 65.900000000000006 83.9 71.5 63.2 67.099999999999994 71.7 65.599999999999994 80.099999999999994 68.2 70.8 73.400000000000006 59.5 53.3 65.400000000000006 79.8 76.900000000000006 90.1 85.2 87.8 85.2 87.5 87.9 82.4 85.7 80.3 88 80.8 84.6 79.900000000000006 86.5 79.900000000000006 86.4 84.3 86.9 75 85.3 81.2 85.8 74.2 87.1 79.2 86.7 93.1 78.8 90.3 84.9 84.2 85.3 69.5 84.4 77.8 80.7 81.7 68.400000000000006 91.8 85.1 73.2 90.4 84.6 88 79.2 89.4 88.5 91.6 91.3 87.6 78.099999999999994 83.5 79.7 81.5 82.3 83.1 84.6 76.8 80.599999999999994 86.8 82.4 85.4 81.900000000000006 80 83.2 80.400000000000006 86 81.900000000000006 82.4 76.099999999999994 89.2 80.8 86.1 88.8 89.5 89 83.1 78.3 85.5 89.3 83.5 83.1 84.6 78.3 88.1 83.4 77.900000000000006 84.8 86.1 84.2 88.8 80 84.6 83.7 72.2 84.5 90.7 83.4 91.4 75.5 82.5 82.9 81.400000000000006 88.5 82.7 83.8 83.5 89 78.599999999999994 83.1 81.2 74.8 83.1 78.7 89.3 79.8 75 83.8 80.5 73.7 85.5 86.6 77 79.5 81.599999999999994 82.8 78.599999999999994 79.7 79.400000000000006 84.4 81.2 78.900000000000006 91.5 77 82 80.400000000000006 91 82.9 83.4 84.9 79 87.7 81.7 84.3 91.4 83.9 81.599999999999994 88.7 86.7 76.400000000000006 88.7 80.400000000000006 86.3 93.2 86.7 85.6 83.6 81.7 81.2 86.7 83.5 90.6 85.5 86.1 86.6 85.6 84.1 80.599999999999994 83.5 79.7 81.900000000000006 80.8 86.4 84.6 84.6 79.8 82.6 84.7 75 79.099999999999994 83.7 81.5 81.3 79.7 82.3 79.099999999999994 90.1 75.8 80 91.1 81.400000000000006 81.3 79 77.599999999999994 82 81.8 87.6 78.8 80.2 80.900000000000006 85.2 81.5 82.5 87.2 91 89.9 79.2 86.2 86.6 84.4 80.400000000000006 79.3 82.2 85.6 79.5 84.8 94 75.900000000000006 84.5 84 88.1 81.900000000000006 73.400000000000006 68.099999999999994 67.2 63.4 58.8 65.3 64.400000000000006 66.599999999999994 59.4 65.099999999999994 71.599999999999994 68.8 68.599999999999994 62.2 69.3 67.2 81.599999999999994 79.3 67.5 69.8 67.400000000000006 63.8 77.900000000000006 80.3 80.400000000000006 59.7 53.7 58.8 65.900000000000006 81 66.7 59.7 66.400000000000006 73.900000000000006 60.5 78.5 83 74.900000000000006 72.900000000000006 64.099999999999994 74.7 61.9 72 75.5 83 66.5 61 65.5 62.1 67.7 72.900000000000006 58.4 80 63.5 74.599999999999994 72 70.3 66.7 64.900000000000006 55.1 81.8 62 60.6 68.8 70.8 74.8 59.3 54.4 71.7 65.5 64.599999999999994 60.5 68.5 67 77 66.5 64.7 67.7 58.1 68.2 69 65 84.6 84.7 80 75.099999999999994 75.7 77.3 76.900000000000006 71.8 70.7 89.2 81.5 70.5 81.5 78.900000000000006 82.9 81.099999999999994 79.099999999999994 66.599999999999994 86.7 74 79.599999999999994 85.9 79.599999999999994 88.7 86.1 85.3 80.3 69.400000000000006 78.5 72.8 79.099999999999994 77 66.3 69.7 63.7 77.7 74 81.8 84.7 79 80.099999999999994 77.3 73.400000000000006 81.900000000000006 81.3 73.400000000000006 65.2 83.4 79.5 79.400000000000006 86 80 72.900000000000006 79.900000000000006 77.400000000000006 79.5 76.400000000000006 80 80.599999999999994 69.400000000000006 77.8 68.599999999999994 74.5 79.400000000000006 82.5 73.900000000000006 61.1 77.599999999999994 78.7 71.099999999999994 74.5 63.6 79.8 87.1 72 75.2 73 58.2 71.2 78.3 79 76 91.8 77.5 85.1 80 78.7 77.099999999999994 79.3 65.2 62.1 89.1 73.099999999999994 73.8 72.400000000000006 88 74 81.400000000000006 76.8 72.900000000000006 67.599999999999994 81 66.900000000000006 80.400000000000006 72.400000000000006 81.400000000000006 71.400000000000006 76.599999999999994 79.5 62.5 59.7 74.8 80.2 71.099999999999994 71.3 89.3 76.400000000000006 78.7 85.2 88.1 83.3 87.1 87.1 84.9 85.3 82.7 84.5 85.7 86.3 87.4 93.3 84.7 78.599999999999994 70.5 87.8 86.8 90.2 87.6 84.2 91.4 75 80.2 86.1 89.8 83.4 83.2 91 82.6 87.6 82.9 82.4 81.599999999999994 83.4 81.900000000000006 78.8 87.4 83.5 80.599999999999994 84.4 81.2 81.2 85.1 87.5 88.9 83.4 81 86.3 83.9 69 76.8 88.5 86.3 85.5 89.5 94.2 93.4 84.4 88.1 83 83.3 89.2 84.1 83.4 89.4 83.5 86.4 85.2 86.7 86.7 72 78.7 87.5 73.5 86.9 73.599999999999994 85.3 82.1 83.5 87.3 82.4 88.2 85.7 88.3 84.2 82 85.2 81.099999999999994 88.9 90.3 83.2 82.2 89.6 85.8 89.1 85.6 84.5 89.7 87.2 84.2 80.400000000000006 88.5 86.6 82.2 84.6 82 90.5 86.3 90.8 91.8 88.6 82.6 85.3 79.400000000000006 80.599999999999994 85.5 84.5 85.6 83.7 87.1 89.1 84.6 84.7 86.6 87.9 81.8 87.4 81.2 93.3 86.8 79.599999999999994 87.5 86.1 82 86.4 86.2 80.900000000000006 83.7 80.400000000000006 84.7 89.7 87 83.6 90.8 87.2 85.1 79.5 91.6 79.099999999999994 78.900000000000006 76.7 78.3 79.2 83 81.5 77.099999999999994 79.2 75.900000000000006 86.7 83.9 82 82.5 85.7 88.2 86.2 76.900000000000006 87.7 87 88.2 90.5 86.4 83 78.2 86.6 87.2 80.3 81.9000000 00000006 68.5 75.599999999999994 84.3 70.5 91.5 81.8 84.4 87.9 90.6 83 73.3 79.400000000000006 89.6 89.8 79.3 84.9 84.4 78.400000000000006 72.599999999999994 75 80.8 78.400000000000006 72.3 70 75 79.400000000000006 68.3 72.2 68.8 67.099999999999994 84.5 96.3 59.8 65.2 69.8 81 73.8 73 75.2 86 76.8 74.5 84.5 76.099999999999994 72.099999999999994 79.099999999999994 77.099999999999994 79.900000000000006 76.099999999999994 86.3 83.2 62.3 83.8 81.2 79.099999999999994 81.2 82.1 80.599999999999994 76.400000000000006 81 82.8 79.900000000000006 84 82.9 80.400000000000006 69.7 77.8 84.4 78.599999999999994 83.4 79.400000000000006 82.9 68.8 81 82.3 83.3 84.9 78.099999999999994 86.7 78.7 83.3 79 85.7 87.4 81.8 76.400000000000006 80.400000000000006 83 90.2 74.400000000000006 84.9 82.6 85.3 79.2 88.2 84.8 81.7 82.4 79.099999999999994 82.8 86.2 76.2 84.8 91.4 81.7 84.6 79.2 82.3 83.6 75.599999999999994 80 76.5 68.7 68 70.2 68.599999999999994 70.599999999999994 75 63.8 70.599999999999994 78.3 81.900000000000006 67.599999999999994 78.2 66.2 82.1 82.1 69.2 74.8 77.900000000000006 73.3 73.099999999999994 76.5 72.2 68.599999999999994 82.1 85 77.599999999999994 88.6 72 78.099999999999994 65.8 83 65.599999999999994 82 73.599999999999994 71.400000000000006 71.400000000000006 68.400000000000006 73 65.400000000000006 83 65.400000000000006 75 77.7 83.2 65.599999999999994 73.5 68.400000000000006 78.400000000000006 78.8 75.900000000000006 72.2 76.3 71.900000000000006 71.7 70.2 77.3 69.3 70.7 86.2 68.599999999999994 64.2 82.6 75.599999999999994 86.3 62.5 84.3 87.6 75.2 76.8 76.8 71.900000000000006 74.900000000000006 79.900000000000006 80.599999999999994 70 69.2 64.900000000000006 68.900000000000006 74.2 70.400000000000006 69.099999999999994 71.400000000000006 73.400000000000006 73.2 67 70.5 82.5 66.3 80.2 68.099999999999994 89.3 67.5 69.900000000000006 81.599999999999994 77.2 66 69.400000000000006 72 71.099999999999994 83.1 85 73.8 77.8 81.3 82.2 78.8 87.9 90.9 78.8 79.599999999999994 80.400000000000006 77.5 75.5 65.900000000000006 78 87.4 89.2 73.400000000000006 78.7 74.8 72 75.3 66 76.900000000000006 59.3 79.099999999999994 79 79 80.2 77.900000000000006 81.400000000000006 79.900000000000006 79.8 76.7 80.099999999999994 81.3 84.1 83.2 73.7 81.099999999999994 67.8 78.5 82.5 79.900000000000006 86.1 81.099999999999994 81.900000000000006 83.7 76.599999999999994 87.4 72.599999999999994 82.5 68.599999999999994 82.5 83.3 79.900000000000006 82.9 85.7 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34783 29112 34255 35236 28755 33930 34331 62055 35298 32034 44708 36477 35252 45315 45858 43756 22186 26474 25663 40107 50356 31463 23747 28107 37056 30892 36710 48438 39607 36681 34828 46555 27700 35116 41352 60464 31609 37017 39014 32530 36430 36990 28745 32052 34480 39793 35000 31618 41264 36618 26565 57859 34353 28687 36486 39700 39256 32144 28615 46131 37718 36450 29955 42071 29537 45127 33157 33364 37118 24367 36374 33875 31918 34341 52377 39853 41267 37210 37685 39560 34301 39213 48254 44674 35050 40215 50346 46136 46932 39446 29431 63801 34363 41560 49026 37920 62237 53589 55256 45458 39726 37456 35202 39719 40748 35005 33364 32025 55964 45116 37010 43970 35186 36954 39840 32628 37925 40696 32991 33573 50561 40322 59650 45559 34916 38055 49220 40214 39457 54828 36356 41567 34770 38870 32956 41097 40902 38155 39876 29623 47846 39740 42187 39467 34533 45108 40911 28783 50932 33291 28206 47156 40964 37818 41673 71894 38176 44086 33833 47751 40503 53919 33298 29300 73708 32595 50462 40162 65049 42150 35252 35283 40359 26876 37908 34740 42013 33607 39775 31597 38646 52800 34901 30904 41102 35363 31784 34958 37283 35637 32500 42080 41372 33872 42443 37525 38619 35151 40412 33862 38547 39145 44368 49072 33363 35942 35153 35803 39624 53430 37642 36997 48093 38984 34440 38256 38919 37814 34941 44352 32861 40857 31033 36948 39216 36556 39423 32763 41183 41335 31969 46211 34566 37998 39136 50468 41737 38872 38836 38400 39879 31528 36332 47278 47836 38765 35240 40342 32540 40478 50675 33566 36502 47349 43709 46769 59878 43041 41645 37676 43044 44101 46148 42720 39490 49991 37944 46512 42456 44027 47872 55623 34770 45264 37723 42530 39260 44937 34059 35281 47407 44825 36527 47594 51848 39493 34328 36414 39569 35874 42873 42003 41785 50522 41612 32068 39373 35483 53873 47074 42641 33791 33148 46094 45005 38921 40250 41950 37277 48019 37331 44032 48040 41501 50666 48684 41570 38469 33206 46232 69261 54289 41214 54967 37954 36876 38427 47213 39571 35133 36263 35949 62434 41664 38652 34462 47749 52532 57434 66745 62283 42742 53316 60692 59302 41166 52391 42340 46373 52354 58559 58977 47228 53820 56132 51479 54558 43244 54017 68721 62462 74856 57674 52699 56555 83984 75446 61915 53540 50397 57856 69865 51869 102839 72877 79099 82735 99559 59786 63348 58666 99035 84016 71237 72217 49931 30756 36705 35753 39576 37225 32750 38372 41191 37504 31903 33612 31949 38360 43621 101687 26755 32189 31562 39727 32046 37884 34224 57862 43462 34144 54333 31091 30173 34450 39193 36147 43895 55270 41330 35543 45502 43001 48257 43070 46877 43355 47666 53957 44236 41787 68337 49647 44827 40572 43334 52189 46977 41563 42383 43776 41367 44233 54151 51728 57788 41358 92724 60541 49092 46225 52582 57386 67014 48881 47112 43052 93044 54631 55231 70851 87498 41652 63669 53730 47096 46355 47810 45672 84045 47627 51834 47980 54776 50459 48490 56843 81849 51356 44592 50421 49798 37646 38424 37105 39426 39991 32410 34599 46198 47200 45865 59396 46006 50839 49360 45078 52182 55162 36034 39813 40417 45419 34506 46299 48230 52550 54595 49741 51716 38477 55787 39884 54191 50163 50825 45888 34300 51447 41289 54862 34060 45190 43667 49057 34013 42777 36616 53963 41904 52614 39754 50076 40152 53321 41703 41372 39887 37065 65110 39273 42356 53088 47819 51713 34309 43454 54545 43876 39190 46216 38024 47834 42311 46676 49365 37113 36304 43490 48266 40063 40927 39919 47498 49957 42540 36827 49673 33063 65186 40293 70786 36496 37158 41980 43693 44100 42630 47192 38199 37433 40120 34355 42052 38429 41072 32607 53177 49106 41023 37629 38733 38638 36871 33623 41218 38576 46066 29820 38068 37600 32683 38242 36026 35110 33970 37772 41627 54412 47666 34883 37192 47179 46896 34144 45828 48495 39579 46469 33768 47904 31474 28942 31754 41870 46030 43572 42146 48203 43568 43343 41057 40538 37737 47692 50435 45837 35171 55826 38251 49307 61642 45710 55532 51929 63574 52093 44059 44670 46635 50421 50600 57848 86581 55027 61741 47289 55011 56736 38865 77495 62634 38760 52733 56455 44334 39028 54912 45458 44104 47558 52210 39470 39717 50046 62772 37495 56800 53396 57982 48922 56914 45374 49830 71845 35126 55021 56781 39220 51692 37162 52627 45293 42403 56929 51913 44261 55137 40741 57087 54186 59764 48141 47780 52243 36054 48965 57293 51265 54458 49301 45685 66608 50844 37930 74601 44122 53471 52438 57210 49997 32029 38952 31863 47263 35274 36502 35900 35204 58493 37853 34160 29277 39423 53868 30515 43597 35027 39902 42697 36719 36039 36266 35981 42488 36134 41998 37302 33203 28790 43388 31607 29120 39567 30475 31657 39600 47213 33538 30846 35115 40147 47352 41912 47984 31104 33423 39840 34032 40067 38997 36608 43727 37936 31312 45136 35596 44382 35410 40757 36988 36918 34699 40644 28484 38719 57247 32913 35549 39531 46178 31961 49191 53737 46106 38056 37237 43229 39091 53934 67042 46730 58954 40604 45295 38769 53869 42768 43267 41914 39851 49337 46936 46153 40201 40597 37983 47555 42183 48297 38929 51896 48300 53137 54467 45238 44114 46663 43431 41359 46290 67096 37010 56784 54972 49341 40623 47623 42134 57560 42302 45104 76886 54463 38849 41466 45201 46555 84054 39610 40366 39988 43889 43201 60125 53432 64483 48338 47150 35337 35505 52104 44903 39072 42884 38919 40835 44666 44332 58581 42676 52570 55931 43473 43788 42532 44625 41419 59546 78305 49014 58229 40310 53949 39579 57423 41519 42093 46318 39791 38978 43281 41219 51924 41524 46449 48411 43873 47766 46812 58273 65313 61297 64941 47565 68359 42011 48774 26902 47381 30904 36805 60492 51373 42141 48672 43494 41740 37953 34925 38275 40018 34281 55760 45243 39103 45241 45457 52971 44672 37037 46947 39555 49952 44654 43682 34637 57489 40649 34147 34239 42309 47200 38061 46618 51441 46052 48375 42838 40474 31170 57335 38339 39275 32585 39448 45619 45077 41670 16338 37383 37065 33547 38886 35446 46673 26588 46733 43093 38911 40920 29958 36659 41457 38144 38924 42594 29263 38482 43576 41679 42544 32182 55315 38652 40039 30824 39507 38989 40243 43880 40878 62225 36699 45565 28810 39349 47619 29890 38000 54795 45656 48254 35722 38729 36459 42963 26925 40829 52998 41837 25791 36473 46418 57658 35830 45537 23252 45677 47281 36918 37308 48739 45099 32549 42235 39215 35234 59004 44217 33189 30841 32894 44924 38638 39779 51230 36998 39081 50276 42208 51851 29914 46399 40041 44829 36040 39110 29555 41644 50114 25437 37474 35811 40292 35621 41267 38836 39923 38578 46067 34116 42254 29694 48214 28314 38298 39260 39190 43039 52008 41089 38817 38448 47607 40445 49505 53540 37787 39053 50180 47103 35673 42177 34647 36123 31761 38159 39795 39157 42772 55577 59617 31015 39853 44693 50968 45860 41600 43162 59254 53881 41466 38442 35188 36257 39803 42630 34211 38629 37824 88957 64545 41138 43814 43518 39522 49579 49167 42585 49709 35917 50221 56098 31702 36549 47465 49339 50679 37595 44001 42482 62604 37465 35254 38512 23972 39873 42514 48815 47080 46148 41789 33669 40117 51859 36612 39416 61744 37734 35345 46005 35433 37441 33029 91185 32746 41740 59405 36587 40309 48465 46341 32756 41443 37788 33172 33318 35975 55771 36316 38105 37452 74941 36963 33338 28214 37339 28856 34541 40102 32566 64815 39972 39530 34228 44413 44445 35605 34565 33229 82169 41135 40270 31544 39175 54606 35022 49057 45898 44027 36518 40380 47859 45063 41554 56575 40266 29628 40099 45619 36446 48418 54836 43150 59636 30496 57936 45642 41879 32006 40678 40015 56213 41368 36197 39655 27091 47311 47099 48273 41837 45382 39780 41466 44677 33255 37129 57440 38068 34147 57649 63748 32182 39176 44132 37841 45860 36456 37734 32765 40690 35913 46569 28136 37501 46703 39882 49382 37803 41147 41267 44836 51492 41448 34363 33090 43201 41837 37870 32629 40982 39804 41417 27332 46424 31876 50310 42720 39364 32696 39968 65477 44865 37346 36492 36432 40251 36688 33739 46290 48934 43398 48384 40167 41076 58568 39665 36087 39256 37965 25566 43397 54983 42778 32334 35475 30002 38601 57660 37185 83885 35794 42349 35012 34789 41477 44844 38753 38292 40738 39235 37476 42711 47820 50724 21245 38082 45221 35960 44263 38420 59446 43813 31177 36160 36401 41775 42671 60195 34847 38372 42927 37302 34968 36528 45093 49859 40508 49092 37828 47321 36173 41461 39943 43485 37975 28467 78064 51499 39380 53980 42333 42058 39261 31712 21683 44468 57452 51144 43814 39691 69161 40290 51299 45287 41691 42627 49096 44086 46572 64716 38136 51190 62270 36220 42535 46113 83625 58923 44435 59000 63865 47903 41193 56659 55536 51396 44798 61369 39249 53627 55396 50663 51305 40014 47299 52743 49180 52377 38941 65329 49619 51816 48136 46995 81101 55411 45072 55529 39130 62731 40277 28595 38467 47990 51292 39387 55025 37240 75354 66425 48034 58301 40956 30163 53528 48138 104335 79811 40659 59694 48989 60427 44961 58470 72483 36914 59127 41196 38527 76237 63315 40956 38274 58426 71566 46267 64213 64205 42788 29572 103817 50722 35914 51306 55639 40395 47469 41618 47332 68992 36399 49083 39734 55211 42943 36952 45252 69503 40293 64206 84910 43604 59142 42514 61390 46388 52455 34543 35193 50427 38726 43761 74051 86003 48348 39915 35148 54609 42148 46081 33661 41496 74606 72158 37064 35258 41721 39915 65321 33585 55642 39037 34628 39047 87075 96449 40790 44521 36348 50889 38553 42733 37308 41495 77764 78260 35325 47111 40955 29335 37140 78422 43436 31737 40062 39544 50200 42405 52927 62697 4207 6 47749 44199 43624 43155 60559 48037 46920 62274 43124 51230 49514 39118 50193 42993 45410 43974 58588 48748 68429 60297 41896 44112 45713 45383 50959 38266 40175 40778 58191 55986 54557 50612 68304 48026 44634 60470 50776 46214 51498 36796 44834 31833 49899 33043 31425 42456 36661 27777 28475 34427 31909 29424 37223 34663 40763 43458 40995 39342 41752 57122 43467 34842 29173 31671 21795 36850 39892 34929 34278 40098 27480 36849 35497 45076 34723 39695 39171 42141 33986 35950 53927 36277 35142 35184 31553 27222 34916 33791 37705 34722 35210 27104 39822 39582 42847 30807 43006 40714 47984 42983 59791 47887 44049 67672 50972 44511 58010 43942 63364 58173 49964 45346 49886 50486 44733 58672 41223 46687 55647 50799 54733 38078 47649 60375 45486 60464 56414 50812 47913 42697 50359 55722 58140 45385 46015 37898 49046 47849 53038 48427 63866 80771 48414 63787 53014 55980 45376 61866 43765 58594 40349 70711 53990 41563 49006 59520 49563 48774 42710 43458 59568 43402 73418 80892 52663 47630 57214 53545 37061 42071 63767 46420 50981 45829 41841 41487 38475 43783 50986 52514 47139 38234 46122 43595 44460 50261 59907 70304 57341 44982 41641 12729 14655 14773 16679 16381 16246 16086 14783 15069 14575 25567 17481 21269 16951 16779 27337 16544 17317 21163 14136 20026 15530 14021 15172 21894 21189 19837 14319 12514 15592 14625 33741 21177 15934 21556 18466 15042 14443 16596 16827 14655 12467 12193 18823 14418 17547 16472 11898 14981 15158 14509 15563 14754 16071 12802 15475 15697 16732 15718 14752 19317 16072 14664 16849 22356 15738 14111 15312 25918 23597 28295 12806 17372 17936 12012 15097 15823 15350

SUMMARY OUTPUT

Regression Statistics

Multiple R0.62531446

R Square0.391018174

Adjusted R Square0.390828873

Standard Error9501.216664

Observations 3219

ANOVA

dfSSMSFSignificance F

Regression 11.86467E+111.86467E+112065.587858 0

Residual 32172.90409E+1190273118.09

Total 32184.76876E+11

CoefficientsStandard Errort StatP-valueLower 95%Upper 95%Lower 95.0%Upper 95.0%

Intercept28620.5667394.194336772.60522042 027847.6692329393.4641827847.6692329393.46418

Bachelors (%)984.066363621.6522259945.4487388 0941.6128091026.519918941.6128091026.519918