Consider the model output below. Use it to answer Questions 12 – 14. Regression
ID: 3155496 • Letter: C
Question
Consider the model output below. Use it to answer Questions 12 – 14.
Regression Analysis: Avg. Tot. Score versus Avg. Salary, %Takers
Model Summary
S R-sq R-sq(adj) R-sq(pred)
33.6877 80.56% 79.73% 78.08%
Coefficients
Term Coef SE Coef T-Value P-Value VIF
Constant 987.9 31.9 30.99 0.000
Avg. Salary 2.18 1.03 2.12 0.039 1.61
%Takers -2.779 0.228 -12.16 0.000 1.61
Prediction for Avg. Tot. Score
Variable Setting
Avg. Salary 40
%Takers 50
Fit SE Fit 95% CI 95% PI
936.181 6.34430 (923.418, 948.945) (867.219, 1005.14)
12. Under what conditions are the confidence and prediction intervals computed above valid?
13 Assuming that these conditions are satisfied, which of the following statements is accurate?
a.) We are 95% confident that a state with an average teacher salary of $40,000 and 50% of eligible students taking the SAT will have an average total SAT score between 923.418 and 948.945.
b.) We are 95% confident that a state with an average teacher salary of $40,000 and 50% of eligible students taking the SAT will have an average total SAT score between 867.219 and 1005.14.
c.) Neither of the above.
14 What is the expected average total SAT score for a state with average teacher salary of $30,000 and 50% of eligible students taking the SAT?
Explanation / Answer
12. Under what conditions are the confidence and prediction intervals computed above valid?
condittions : that the sample size are bigger or normal distributed
13)
a.) We are 95% confident that a state with an average teacher salary of $40,000 and 50% of eligible students taking the SAT will have an average total SAT score between 923.418 and 948.945.
14)
Y = 987.9 + 2.18 * 30000 - 2.779* 0.50
Y = 66386.51