The output on the following page was obtained from a regression analysis on sala
ID: 3206193 • Letter: T
Question
The output on the following page was obtained from a regression analysis on salary and years of experience. Use it to answer the questions below. (a) What is the estimated regression line for these data? In terms of salary and years of experience, how is the slope interpreted here? (b) With 95% confidence, what is the slope in the population of interest? (c) At the bottom of the output are two intervals marked “CI” (confidence interval) and “PI” (prediction) interval. Provide an interpretation of each of these intervals.
Variable N Mean Variance Minimum Maximum Salary 64 58.59 583.18 29.00 163.70 YrsExp 64 7.833 52.266 0.140 29.540 Analysis of Variance SS MS F-Value P-Value Source DF 1 21380.1 21380.1 86.30 0.000 Regression 1 21380.1 21380.1 86.30 0.000 YrsExpo 62 15359.9 247.7 Error 63 36740.1 Total Model Summary S R-sq R-sq adj) R-sq(pred) 15.7398 58.19% 57.52% 52.91% Coefficients Coef SE Coef T-Value P-Value Term Constant 38.63 2.91 13.26 0.000 YrsExp 2.548 0.274 9.29 0.000 Regression Equation Salary 38.63 2.548 YrsExp YrsExp 15 95% CI 95% PI Fit SE Fit 76.8568 2.78133 (71.2970, 82.4166) (44.9060, 108.808)Explanation / Answer
Result:
The output on the following page was obtained from a regression analysis on salary and years of experience. Use it to answer the questions below.
(a) What is the estimated regression line for these data? In terms of salary and years of experience, how is the slope interpreted here?
Salary = 38.63+2.548*years of experience
When Experience increases by one year, salary increases by 2.548.
(b) With 95% confidence, what is the slope in the population of interest?
T value with 62 df at 95% level =1.999
Lower limit of 95% CI for slope = 2.548-1.999*0.274 =2.000274
Upper limit of 95% CI for slope = 2.548+1.999*0.274 =3.095726
(c) At the bottom of the output are two intervals marked “CI” (confidence interval) and “PI” (prediction) interval. Provide an interpretation of each of these intervals.
A confidence interval of the prediction of salary is a range that is likely to contain the mean response of salary given specified value of the years of experience in the model.
A prediction interval is a range that is likely to contain the for salary of a single new observation given specified value of years of experience.
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