A sales manager collected the following data on x = years of experience and y = annual sales ($1,000s). The estimated regression equation for these data is
ŷ = 80 + 4x.
Salesperson | Years of Experience |
Annual Sales ($1,000s) |
---|---|---|
1 | 1 | 80 |
2 | 3 | 97 |
3 | 4 | 97 |
4 | 4 | 102 |
5 | 6 | 103 |
6 | 8 | 101 |
7 | 10 | 119 |
8 | 10 | 118 |
9 | 11 | 127 |
10 | 13 | 136 |
(a) Compute SST, SSR, and SSE.
SST=
SSR=
SSE=
(b) Compute the coefficient of determination r2. (Round your answer to three decimal places.)
r2=
Comment on the goodness of fit. (For purposes of this exercise, consider a proportion large if it is at least 0.55.) Chose one of the following.
1.The least squares line provided a good fit as a large proportion of the variability in y has been explained by the least squares line.
2.The least squares line did not provide a good fit as a large proportion of the variability in y has been explained by the least squares line.
3.The least squares line did not provide a good fit as a small proportion of the variability in y has been explained by the least squares line.
4.The least squares line provided a good fit as a small proportion of the variability in y has been explained by the least squares line.
(c) What is the value of the sample correlation coefficient? (Round your answer to three decimal places.)
The statistical software output for this problem is:
Hence,
a) SST = 2502
SSR = 2272
SSE = 230
b) r2 = 0.908
The least squares line provided a good fit as a large proportion of the variability in y has been explained by the least squares line.
c) Correlation coefficient = 0.953
A sales manager collected the following data on x = years of experience and y =...
A sales manager collected the following data on x = years of experience and y = annual sales ($1,000s). The estimated regression equation for these data is ý = 81 + 4x. Salesperson Years of Experience Annual Sales ($1,000s) 1 107 103 101 119 8 9 10 10 11 13 123 127 136 (a) Compute SST, SSR, and SSE. SST = SSR = SSE = (b) Compute the coefficient of determination 2. (Round your answer to three decimal places.) 12...
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