Question

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

1. Develop a scatter diagram for these data with salary as the independent variable, x and bonus as the dependent variable, y.

2. What does the scatter diagram developed in part a) indicate about the relationship between salary and bonus?

3. 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.

4. Provide an interpretation for the slope of the estimated regression equation.

5. Predict the bonus for a vice president with an annual salary of $120,000.

6. Compute SST, SSR, and SSE

7. Compute the coefficient of determination r2. Comment on the goodness of fit.

8. What is the value of the sample correlation coefficient?

9. Develop the null and alternative hypothesis to test the linear relationship between salary and bonus

10. At the .05 level of significance, determine whether salary and bonus are linearly related. Use the t test.

11. Solve the problem in Excel and compare your results.

Answer 1

( a )

  

( b )

There is strong positive relationship  between salary and bonus.

( c )

Find X⋅Y and X² as it was done in the table below.

X	Y	X⋅Y	X⋅X
135	12	1620	18225
115	14	1610	13225
146	16	2336	21316
167	19	3173	27889
165	22	3630	27225
176	24	4224	30976
98	7	686	9604
136	17	2312	18496
163	18	2934	26569
119	11	1309	14161

y = −10.164 + 0.184⋅x

( d )  interpretation for the slope

The slope indicates that every​ 1-unit increase in salary increases the bonus of this model by ​$
0.184, on average

( e )

Given x = 120,000

y = -10 .164 + 0.184 ( 120000)

y = 22069.836