A university has studied the relationship between the GPA (grade point average) of its graduates and StartSal, their starting salaries (in thousands of dollars). A sample of seven graduates was randomly selected.
The data collected and output from Excel are shown below:
MKTGrad GPA StartSal (in thousands)
1 3.26 33.8
2 2.60 29.8
3 3.35 33.5
4 2.86 30.4
5 3.82 36.4
6 2.21 27.6
7 3.47 35.3
Regression Statistics
Multiple R 0.988215019
R Squared 0.976568924
Adjusted R Squared 0.971882709
Standard Error 0.536320693
Observations 7
Coefficients Standard Error t-stat P-value lower 95% Upper 95%
Intercept 14.8156153 1.234862598 11.99778447 7.09585E-05 11.64130512 17.98
X Variable 1 5.706568981 0.395307208 14.43578278 2.87759E-05 4.690401113 6.722
a) From the scatter plot that the data would show, explain why you think a linear regression model is or is not appropriate for these data? Explain.
b) Write the general for of the simple linear regresion model
c) What does the model predict for a student with a GPA of 3,25?
d) 1)What does the model predict for a student with a GPA of 0?
2)Is this prediction useful or not?
e) Let Ho denote the true coeffecient Beta1 of the independent variable is equal to zero at the significance level 0.001. Explain why you can reject Ho or fail to reject Ho?