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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.
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.
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.
k) Solve the problem in Excel and compare your results.
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