Random Error Standard Deviation

First, we have to figure out the least squares line that relates y (work-life balance score for each MBA alumnus) to x (average number of hours worked per week), which is y= β0 + β1x + . For the GMAC data, the slope (β1) is -0.347 whereas the intercept (β0) is 62.499.

By plugging in the slope and the intercept, the least squares line would be: y= 62.499 + (-0.347) x. This least squares line indicates that the estimated mean work-life balance score decreases by -0.347 average number of hours per week.

Next, we have to interpret the random error component ( ) of the least squares line. The estimate of error standard deviation for this particular data set is 12.28455 which suggests that the work-life balance score (y) values should be two times of the standard deviation. This can be best expressed as in the equation of 2s = 2(12.28455) which equals 24.57 average hours per week.

Then, we can analyze the accuracy of hypothesis model to see if the average number of hours per week (x) helps figure out y by using the least squares line. We test the null hypothesis that the slope (β1) is equal to 0 or less than 0. In other words, it means that average number of hours per week and work-life balance score do not have a linear relationship.
These statements can be best demonstrated as: H0: β1 = 0 and Ha: β1 < 0. For this data, the two-tailed significance level for the test Ha: β1 ≠ 0, is roughly 0 because when we divide the p-value in half, the p-value for the one-tailed test is also about 0. Therefore, this concludes that there is no linear relationship between x (average number of hours) and y (work-life balance score). We can also reject the alternative hypothesis of work-life balance score increases as average number of hours per week increases since the p-value is relatively