As part of a study to investigate the relationship between stress and certain other variables, the following data were collected on a simple random sample of 15 corporate executives.

(a) Find the least-squares regression equation for these data.

(b) Construct the analysis of variance table and test the null hypothesis of no relationship among the five variables.

(c) Test the null hypothesis that each slope in the regression model is equal to zero.

(d) Find the multiple coefficient of determination and the multiple correlation coefficient. Let a ¼ :05 and find the p value for each test.

Measure of Stress (Y)

Measure of Firm Size

(X1)

Number of Years in Present Position (X2)

Annual Salary

(1000)

(X3) Age (X4)

101 812 15 $30 38 60 334 8 20 52 10 377 5 20 27 27 303 10 54 36 89 505 13 52 34 60 401 4 27 45 16 177 6 26 50 184 598 9 52 60 34 412 16 34 44 17 127 2 28 39 78 601 8 42 41 141 297 11 84 58 11 205 4 31 51 104 603 5 38 63 76 484 8 41 30 For each of the studies described in Exercises 12 through 16, answer as many of the following questions as possible:

(a) Which is more relevant, regression analysis or correlation analysis, or are both techniques equally relevant?

(b) Which is the dependent variable?

(c) What are the independent variables?

(d) What are the appropriate null and alternative hypotheses?

(e) Which null hypotheses do you think were rejected? Why?

(f) Which is the more relevant objective, prediction or estimation, or are the two equally relevant?
Explain your answer.
(g) What is the sampled population?
(h) What is the target population?
(i) Which variables are related to which other variables? Are the relationships direct or inverse?
(j) Write out the regression equation using appropriate numbers for parameter estimates.
(k) What is the numerical value of the coefficient of multiple determination?
(l) Give numerical values for any correlation coefficients that you can.