The chairman of the marketing department at a large state university undertakes

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 recent marketing graduates are randomly selected, and the data shown below on the left are obtained. The MINITAB output obtained by fitting a least squares regression line to the data is below on the right.

Find b1 and b0. Interpret the meanings of b0 and b1. Does the interpretation of b0 make practical sense? (Round your answers to 3 decimal places. Leave no cells blank - be certain to enter "0" wherever required.)

Use the least squares line to compute a point estimate of the mean starting salary for all marketing graduates having a grade point average of 3.25 and a point prediction of the starting salary for an individual marketing graduate having a grade point average of 3.25. (Round your answer to 5 decimal places.)

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 recent marketing graduates are randomly selected, and the data shown below on the left are obtained. The MINITAB output obtained by fitting a least squares regression line to the data is below on the right.

Explanation / Answer

(a) From the regression equation, Salary Y = 13.34 + 6.10 GPA

    b0 = Y - Intercept = 13.34

     b1 = Slope = 6.10

i. The estimated regression line obtained in our model, we get the predicted value of y for x = 0 as

       ycap = 13.34 + 6.10 (0) = 13.34 thousands of dollars

Thus, we can stat that a student has 0 GPA is expected to salary 13.34 thousands of dollars. The point estimate of the average salary for all students with zero GPA is 13.34 thousands of dollars.

    ii) b1 = 6.10, that means, x increased by one unit, yhat increased by 6.10 which is the value of b1.

        b1 is positive, an increase in x will lead to an increase in y and vice versa. both variables move same direction. Such relationship between X and Y is called Positive linear relationship.

b) Given GPA = 3.25

ycap = 13.34 + 6.10 (3.25) = 33.165 thousands of dollars

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