Question

1. Wageweb conducts surveys of salary data and presents summaries on its website. Based on salary data as of October 1, 2002, Wageweb reported that the average annual salary for sales vice presidents was $142,111, with an average annual bonus of $15,432. Assume the following data are a sample of the annual salary and bonus for 10 sales vice presidents. Data are in thousands of dollars. Vice President Salary Bonus 1 135 12 2 115 14 3 146 16 4 167 19 5 165 22 6 176 24 7 98 7 8 136 17 9 163 18 10 119 11 a) Develop a scatter diagram for these data with salary as the independent variable, x and bonus as the dependent variable, y. b) What does the scatter diagram developed in part a) indicate about the relationship between salary and bonus? c) Use the least squares method to develop the estimated regression equation. We can call intercept for the regression line, b0 and slope of the regression line, b1. d) Provide an interpretation for the slope of the estimated regression equation. e) Predict the bonus for a vice president with an annual salary of $120,000. f) Compute SST, SSR, and SSE g) Compute the coefficient of determination r2. Comment on the goodness of fit. h) What is the value of the sample correlation coefficient? i) Develop the null and alternative hypothesis to test the linear relationship between salary and bonus j) At the .05 level of significance, determine whether salary and bonus are linearly related. Use the t test. k) Solve the problem in Excel and compare your results.

Answer 1