Question: The chairman of the marketing department at a large state university undertakes a study to relate starting salary (y) after graduation for marketing majors to grade point average (GPA) in major courses. To do this, records of seven marketing graduates are randomly selected. Following are the results of the analysis of the seven observations.

The regression equation is

SALARY = 14.8 + 5.71 GPA

Predictor Coef SE Coef T P

Constant 14.816 1.235 12.00 0.000

GPA 5.7066 0.3953 14.44 0.000

S = 0.536320 R-Sq = 97.7% R-Sq(adj) = 97.2%

Analysis of Variance

Source DF SS MS F P

Regression 1 59.942 59.942 208.39 0.000

Residual Error 5 1.438 0.288

Total 6 61.380

Obs GPA SALARY Fit SE Fit Residual St Resid

1 3.26 33.800 33.419 0.215 0.381 0.78

2 2.60 29.800 29.653 0.278 0.147 0.32

3 3.35 33.500 33.933 0.229 -0.433 -0.89

4 2.86 30.400 31.136 0.221 -0.736 -1.51

5 3.82 36.400 36.615 0.355 -0.215 -0.53

6 2.21 27.600 27.427 0.400 0.173 0.48

7 3.47 35.300 34.617 0.254 0.683 1.45

Predicted Values for New Observations

New

Obs Fit SE Fit 95% CI 95% PI

1 33.419 0.215 (32.867, 33.971) (31.934, 34.904)

2 29.653 0.278 (28.938, 30.367) (28.100, 31.206)

3 33.933 0.229 (33.344, 34.521) (32.434, 35.432)

4 31.136 0.221 (30.569, 31.704) (29.645, 32.627)

5 36.615 0.355 (35.701, 37.528) (34.961, 38.269)

6 27.427 0.400 (26.400, 28.455) (25.708, 29.147)

7 34.617 0.254 (33.964, 35.271) (33.092, 36.143)

Values of Predictors for New Observations

New

Obs GPA

1 3.26

2 2.60

3 3.35

4 2.86

5 3.82

6 2.21

7 3.47

Suppose that all assumptions have been checked and are not violated. Answer the following questions (assume a Six Sigma Black Belt is asking the question).

a. Why does “SE of Fit” change for each observation?

b. Explain the reason for the different widths of the CI and PI for a given observation.

c. Why is PI the narrowest for the data observation #1?

d. The value S in the output is the estimated standard deviation of what?

e. For what range of GPA can this model be used?