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)
= 44,839.1665(Please see excel file)
SSxx = 279,175.2481 (Please see excel file)
SSyy = 476,876,000,000.00 (Please see excel file)
SSxy = 243,852,830.90 (Please see excel file)
b1 = 873.4758 (Please see excel file)
b0 = -22,293.5969 (Please see excel file)
Linear Equation: = b0+b1X; = -22,293.5696+873.475X
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 = 0.6683 (Please see excel file)
This coefficient is 0.66683 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 be seen from the equation, the slope indicates that the income increases when the percent of high school education increases. And we have the coefficient = 0.6683 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:
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Linear Equation:
y = 873.4758x – 22,293.5969
What does the p-value or t-statistic for the relation between income and education imply?
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 = = 0.6683
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?
Question #3:
Problem 3, Page 389 in the text.
High school education(%) vs Median income($)
Income 78.7 82.0 64.7 63.2 70.4 60.5 67.8 73.9 64.2 63.5 66.2 65.0 70.8 66.0 62.9 73.2 73.3 67.7 65.7 68.4 60.1 70.4 77.8 70.3 63.8 77.6 68.5 74.1 66.1 62.1 65.6 64.8 65.2 66.7 76.5 67.0 80.9 65.1 76.4 65.6 81.4 74.5 64.3 70.0 85.4 71.9 63.2 69.4 76.7 67.9 80.3 76.3 62.4 69.7 69.1 61.9 66.5 71.3 86.8 64.8 69.7 70.1 78.8 67.2 72.3 59.5 62.6 74.7 78.5 90.3 71.0 88.9 91.7 76.6 91.8 88.9 93.2 88.5 89.6 85.4 72.2 88.1 74.8 77.4 72.0 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 75.6 82.5 69.3 82.5 77.5 71.2 83.4 72.7 60.7 84.7 65.8 72.4 72.5 77.5 80.4 76.8 66.6 68.7 71.8 64.2 75.3 60.6 74.8 73.1 74.1 73.2 77.3 71.5 69.2 68.3 66.8 65.0 73.1 83.3 71.1 72.2 78.3 77.2 72.1 69.2 73.3 70.7 75.5 73.3 66.0 74.8 67.6 65.3 63.3 56.2 65.0 73.4 69.8 77.6 67.8 76.0 74.3 64.7 63.8 69.8 69.1 70.2 73.5 73.8 62.2 68.8 62.0 72.6 77.4 68.2 84.4 69.2 65.1 82.3 65.4 68.0 76.6 64.6 72.9 68.0 74.5 71.6 79.5 72.9 60.6 64.1 82.4 88.3 84.0 82.3 85.7 64.0 86.9 71.6 89.1 67.5 68.5 84.9 59.0 82.3 68.5 68.8 77.3 79.6 69.9 65.4 91.2 85.1 80.8 63.8 77.1 87.9 68.4 80.4 90.3 79.5 90.5 88.0 75.0 83.3 74.9 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 70.4 73.0 75.7 81.0 61.7 84.3 80.1 79.8 71.8 78.8 82.6 90.7 87.3 78.5 77.2 92.8 88.5 84.1 93.4 72.1 68.2 77.5 90.3 80.1 78.9 76.0 97.0 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 77.0 79.5 91.4 92.3 76.9 81.8 82.3 85.0 91.6 79.6 81.1 80.7 71.4 75.7 93.4 93.3 81.6 96.3 72.0 81.3 88.4 78.1 95.3 70.0 92.1 93.6 79.3 93.3 94.0 81.7 79.6 79.5 84.4 82.4 85.9 88.7 83.0 86.0 89.2 79.6 79.4 85.5 76.5 77.8 88.1 71.9 81.0 74.2 86.3 82.0 69.1 82.1 78.3 86.4 81.8 74.7 63.5 65.9 82.7 82.1 85.9 68.3 70.7 72.4 69.8 72.6 62.9 58.0 54.2 78.5 74.5 80.8 65.2 81.6 69.1 73.2 68.2 79.8 82.3 89.1 73.9 65.6 67.5 81.4 78.2 85.3 67.9 84.9 81.0 88.0 65.1 81.8 79.1 83.6 77.6 84.0 74.8 70.4 87.2 77.7 85.4 87.1 88.7 77.3 73.2 70.0 72.5 82.0 78.4 76.0 71.2 67.3 56.3 67.7 66.0 72.6 65.4 73.3 71.8 65.8 66.0 77.2 71.7 72.5 67.5 79.0 77.9 64.9 69.8 65.5 83.3 56.9 71.1 76.0 65.1 80.2 88.8 60.4 84.4 81.0 64.3 80.1 58.9 88.8 64.8 64.9 87.9 64.6 81.6 67.3 65.9 67.0 79.5 69.7 85.1 66.3 68.5 73.7 81.1 68.4 60.5 78.9 67.2 61.4 65.7 70.9 92.4 71.5 85.7 67.0 84.0 66.0 66.1 82.2 65.9 69.4 70.1 87.3 70.9 70.5 62.2 63.0 79.0 71.1 66.0 84.2 84.3 67.7 68.1 69.7 63.3 58.5 62.0 62.4 77.9 71.3 67.0 70.3 81.3 86.8 71.0 74.3 77.7 72.0 66.7 71.2 63.2 70.8 65.4 65.8 69.0 65.3 77.7 71.4 74.0 61.1 78.9 74.7 86.7 72.1 80.8 73.4 70.2 69.8 75.3 63.3 73.4 75.5 57.8 75.4 62.4 78.0 82.4 70.0 66.9 67.9 67.8 71.1 63.2 69.9 64.8 56.2 66.3 63.6 63.6 64.5 73.5 67.9 67.3 75.1 61.8 73.0 67.7 63.2 74.2 66.7 66.8 73.5 70.3 57.1 68.3 70.1 61.3 67.9 76.0 63.0 68.2 65.0 70.4 68.3 84.6 84.8 39.5 83.3 83.4 90.8 80.8 87.5 85.5 79.8 80.6 90.2 86.3 85.6 87.8 80.0 82.6 88.4 76.0 86.6 76.9 64.0 80.1 84.5 87.2 88.2 80.4 79.4 72.6 82.9 84.4 75.1 87.3 91.0 82.5 84.2 77.4 88.5 73.7 85.5 86.4 67.6 74.5 74.7 77.9 87.3 81.3 88.9 76.6 83.7 67.0 72.8 80.8 63.3 84.1 79.9 83.3 80.0 91.0 81.0 80.0 75.9 77.4 82.9 77.7 79.3 80.2 87.5 83.5 79.3 90.0 81.4 82.3 83.4 72.2 86.0 76.7 78.3 73.6 78.9 86.9 74.3 85.7 68.1 82.4 84.5 80.3 85.2 82.6 77.0 82.5 83.6 67.1 80.2 79 .8 89.9 81.8 86.6 81.4 81.3 80.2 78.1 80.4 86.9 89.2 90.7 83.2 82.1 84.3 79.1 85.0 79.9 76.5 88.3 84.9 87.2 77.1 79.9 78.8 83.1 83.8 72.3 88.7 79.6 75.8 70.7 83.8 71.3 83.4 82.6 80.9 76.1 88.1 83.6 83.1 82.9 83.4 84.1 85.0 74.8 78.7 82.2 82.3 79.1 75.2 74.6 79.8 86.9 79.8 81.4 87.8 80.0 85.7 83.8 86.3 81.3 88.3 83.6 83.2 81.8 79.9 82.3 80.1 70.6 71.8 82.0 79.1 84.7 81.6 80.2 75.7 73.7 82.4 80.7 76.1 80.2 80.9 79.2 79.2 94.2 87.8 80.3 88.5 79.6 83.3 85.0 79.8 82.4 78.5 81.0 76.2 85.7 81.7 81.6 60.2 80.7 80.6 77.4 80.1 81.6 79.8 74.2 81.9 88.5 85.7 80.7 78.7 77.3 78.4 73.8 74.9 80.5 74.8 75.6 88.3 84.4 79.8 81.2 79.6 78.9 79.6 82.4 71.4 79.8 81.2 72.0 84.3 80.8 71.4 87.8 83.7 79.9 83.1 81.2 81.0 81.7 85.0 86.3 75.2 78.1 87.3 82.1 86.2 87.8 84.5 81.4 81.4 82.5 87.8 86.5 89.0 87.7 84.6 81.3 82.2 85.4 83.7 85.9 87.7 87.3 87.5 83.4 84.4 88.0 82.6 85.6 78.5 89.5 78.9 81.7 85.1 85.8 89.2 85.2 82.2 84.8 85.9 84.0 85.0 85.6 86.5 85.4 87.3 85.8 85.7 85.0 86.1 79.3 86.3 85.0 87.0 81.5 86.8 88.1 93.7 85.3 84.0 85.6 83.6 90.6 79.7 79.1 78.7 87.6 82.6 84.0 82.3 83.2 84.4 81.7 82.2 81.8 80.3 80.7 81.1 85.5 83.7 87.4 86.6 88.3 84.0 86.7 82.8 84.2 86.3 86.6 80.4 93.5 84.2 83.3 87.3 82.7 81.5 90.0 82.5 83.9 84.2 87.3 84.1 81.4 86.0 84.4 83.1 81.9 84.7 85.8 82.3 84.2 84.6 87.3 87.1 81.0 80.3 85.5 87.4 87.0 85.5 86.9 91.3 85.4 84.5 86.4 86.4 80.2 92.4 81.2 80.0 87.2 84.8 67.4 69.9 85.3 86.0 84.5 83.6 71.5 73.6 83.7 80.9 76.7 83.8 85.3 74.8 86.9 87.7 88.9 87.6 94.9 75.8 84.7 85.2 83.0 88.5 86.5 85.0 80.9 86.7 81.8 85.9 84.4 85.1 80.3 87.5 88.1 81.2 84.7 81.9 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 87.0 84.5 85.1 63.7 88.1 87.8 86.6 84.6 82.9 78.0 80.5 86.3 92.7 84.3 89.9 84.0 81.2 77.7 81.1 83.4 74.0 60.1 64.5 80.4 76.3 69.5 59.0 56.6 85.1 75.4 78.0 76.6 69.6 57.5 68.9 76.0 60.7 73.1 77.9 80.8 73.4 68.1 64.4 57.4 77.2 75.0 49.4 53.5 67.0 56.0 80.7 61.7 52.6 58.5 85.8 66.5 61.3 78.8 69.5 68.0 69.4 72.4 73.4 62.8 61.4 75.1 77.2 82.3 58.7 74.2 58.2 78.3 73.4 64.4 71.3 52.9 81.8 79.1 63.8 82.1 58.7 54.1 71.0 63.9 58.2 50.9 52.5 58.5 57.4 64.6 74.3 68.5 68.0 80.3 52.6 70.8 75.2 50.1 70.5 76.9 54.0 73.3 77.9 57.6 75.8 58.0 57.8 70.5 56.4 65.8 79.0 62.9 67.0 86.5 67.9 49.2 72.8 58.3 61.8 56.1 65.6 60.9 57.7 70.9 61.8 80.5 79.1 73.6 75.4 68.0 63.5 72.1 70.7 76.9 80.3 68.8 57.8 70.9 61.3 53.6 82.6 64.7 63.2 79.6 59.4 59.8 75.0 71.9 83.0 78.7 77.0 65.4 68.1 61.4 65.7 64.6 70.3 83.9 57.9 70.7 55.5 61.4 73.1 66.9 65.7 73.6 79.3 69.4 79.8 66.3 68.5 80.4 77.2 63.4 66.6 72.7 74.7 78.6 68.7 69.1 74.6 67.4 61.9 70.8 73.1 80.0 67.5 73.9 76.9 62.0 62.9 65.9 83.9 71.5 63.2 67.1 71.7 65.6 80.1 68.2 70.8 73.4 59.5 53.3 65.4 79.8 76.9 90.1 85.2 87.8 85.2 87.5 87.9 82.4 85.7 80.3 88.0 80.8 84.6 79.9 86.5 79.9 86.4 84.3 86.9 75.0 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 68.4 91.8 85.1 73.2 90.4 84.6 88.0 79.2 89.4 88.5 91.6 91.3 87.6 78.1 83.5 79.7 81.5 82.3 83.1 84.6 76.8 80.6 86.8 82.4 85.4 81.9 80.0 83.2 80.4 86.0 81.9 82.4 76.1 89.2 80.8 86.1 88.8 89.5 89.0 83.1 78.3 85.5 89.3 83.5 83.1 84.6 78.3 88.1 83.4 77.9 84.8 86.1 84.2 88.8 80.0 84.6 83.7 72.2 84.5 90.7 83.4 91.4 75.5 82.5 82.9 81.4 88.5 82.7 83.8 83.5 89.0 78.6 83.1 81.2 74.8 83.1 78.7 89.3 79.8 75.0 83.8 80.5 73.7 85.5 86.6 77.0 79.5 81.6 82.8 78.6 79.7 79.4 84.4 81.2 78.9 91.5 77.0 82.0 80.4 91.0 82.9 83.4 84.9 79.0 87.7 81.7 84.3 91.4 83.9 81.6 88.7 86.7 76.4 88.7 80.4 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 80.6 83.5 79.7 81.9 80.8 86.4 84.6 84.6 79.8 82.6 84.7 75.0 79.1 83.7 81.5 81.3 79.7 82.3 79.1 90.1 75.8 80.0 91.1 81.4 81.3 79.0 77.6 82.0 81.8 87.6 78.8 80.2 80.9 85.2 81.5 82.5 87.2 91.0 89.9 79.2 86.2 86.6 84.4 80.4 79.3 82.2 85.6 79.5 84.8 94.0 75.9 84.5 84.0 88.1 81.9 73.4 68.1 67.2 63.4 58.8 65.3 64.4 66.6 59.4 65.1 71.6 68.8 68.6 62.2 69.3 67.2 81.6 79.3 67.5 69.8 67.4 63.8 77.9 80.3 80.4 59.7 53.7 58.8 65.9 81.0 66.7 59.7 66.4 73.9 60.5 78.5 83.0 74.9 72.9 64.1 74.7 61.9 72.0 75.5 83.0 66.5 61.0 65.5 62.1 67.7 72.9 58.4 80.0 63.5 74.6 72.0 70.3 66.7 64.9 55.1 81.8 62.0 60.6 68.8 70.8 74.8 59.3 54.4 71.7 65.5 64.6 60.5 68.5 67.0 77.0 66.5 64.7 67.7 58.1 68.2 69.0 65.0 84.6 84.7 80.0 75.1 75.7 77.3 76.9 71.8 70.7 89.2 81.5 70.5 81.5 78.9 82.9 81.1 79.1 66.6 86.7 74.0 79.6 85.9 79.6 88.7 86.1 85.3 80.3 69.4 78.5 72.8 79.1 77.0 66.3 69.7 63.7 77.7 74.0 81.8 84.7 79.0 80.1 77.3 73.4 81.9 81.3 73.4 65.2 83.4 79.5 79.4 86.0 80.0 72.9 79.9 77.4 79.5 76.4 80.0 80.6 69.4 77.8 68.6 74.5 79.4 82.5 73.9 61.1 77.6 78.7 71.1 74.5 63.6 79.8 87.1 72.0 75.2 73.0 58.2 71.2 78.3 79.0 76.0 91.8 77.5 85.1 80.0 78.7 77.1 79.3 65.2 62.1 89.1 73.1 73.8 72.4 88.0 74.0 81.4 76.8 72.9 67.6 81.0 66.9 80.4 72.4 81.4 71.4 76.6 79.5 62.5 59.7 74.8 80.2 71.1 71.3 89.3 76.4 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 78.6 70.5 87.8 86.8 90.2 87.6 84.2 91.4 75.0 80.2 86.1 89.8 83.4 83.2 91.0 82.6 87.6 82.9 82.4 81.6 83.4 81.9 78.8 87.4 83.5 80.6 84.4 81.2 81.2 85.1 87.5 88.9 83.4 81.0 86.3 83.9 69.0 76.8 88.5 86.3 85.5 89.5 94.2 93.4 84.4 88.1 83.0 83.3 89.2 84.1 83.4 89.4 83.5 86.4 85.2 86.7 86.7 72.0 78.7 87.5 73.5 86.9 73.6 85.3 82.1 83.5 87.3 82.4 88.2 85.7 88.3 84.2 82.0 85.2 81.1 88.9 90.3 83.2 82.2 89.6 85.8 89.1 85.6 84.5 89.7 87.2 84.2 80.4 88.5 86.6 82.2 84.6 82.0 90.5 86.3 90.8 91.8 88.6 82.6 85.3 79.4 80.6 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 79.6 87.5 86.1 82.0 86.4 86.2 80.9 83.7 80.4 84.7 89.7 87.0 83.6 90.8 87.2 85.1 79.5 91.6 79.1 78.9 76.7 78.3 79.2 83.0 81.5 77.1 79.2 75.9 86.7 83.9 82.0 82.5 85.7 88.2 86.2 76.9 87.7 87.0 88.2 90.5 86.4 83.0 78.2 86.6 87.2 80.3 81.9 68.5 75.6 84.3 70.5 91.5 81.8 84.4 87.9 90.6 83.0 73.3 79.4 89.6 89.8 79.3 84.9 84.4 78.4 72.6 75.0 80.8 78.4 72.3 70.0 75.0 79.4 68.3 72.2 68.8 67.1 84.5 96.3 59.8 65.2 69.8 81.0 73.8 73.0 75.2 86.0 76.8 74.5 84.5 76.1 72.1 79.1 77.1 79.9 76.1 86.3 83.2 62.3 83.8 81.2 79.1 81.2 82.1 80.6 76.4 81.0 82.8 79.9 84.0 82.9 80.4 69.7 77.8 84.4 78.6 83.4 79.4 82.9 68.8 81.0 82.3 83.3 84.9 78.1 86.7 78.7 83.3 79.0 85.7 87.4 81.8 76.4 80.4 83.0 90.2 74.4 84.9 82.6 85.3 79.2 88.2 84.8 81.7 82.4 79.1 82.8 86.2 76.2 84.8 91.4 81.7 84.6 79.2 82.3 83.6 75.6 80.0 76.5 68.7 68.0 70.2 68.6 70.6 75.0 63.8 70.6 78.3 81.9 67.6 78.2 66.2 82.1 82.1 69.2 74.8 77.9 73.3 73.1 76.5 72.2 68.6 82.1 85.0 77.6 88.6 72.0 78.1 65.8 83.0 65.6 82.0 73.6 71.4 71.4 68.4 73.0 65.4 83.0 65.4 75.0 77.7 83.2 65.6 73.5 68.4 78.4 78.8 75.9 72.2 76.3 71.9 71.7 70.2 77.3 69.3 70.7 86.2 68.6 64.2 82.6 75.6 86.3 62.5 84.3 87.6 75.2 76.8 76.8 71.9 74.9 79.9 80.6 70.0 69.2 64.9 68.9 74.2 70.4 69.1 71.4 73.4 73.2 67.0 70.5 82.5 66.3 80.2 68.1 89.3 67.5 69.9 81.6 77.2 66.0 69.4 72.0 71.1 83.1 85.0 73.8 77.8 81.3 82.2 78.8 87.9 90.9 78.8 79.6 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homework_4_air.docx
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