Listed below are amounts of court income and salaries paid to the town justices

Question

Listed below are amounts of court income and salaries paid to the town justices (based on data from the Poughkeepsie Journal). All amounts are in thousands of dollars, and all of the towns are in County. New York, for the prediction interval, use a 99% confidence level with a court income of $800,000. Find the explained variation, unexplained variation, and indicated prediction interval. There is sufficient evidence to support a claim of a linear correlation, so it is reasonable to use the regression equation when making predictions. Explained variation S378.22. unexplained variation 1342.72. prediction interval $7400

Explanation / Answer

Answer:

Explained variation 3210.364 unexplained variation 1087.191 , prediction interval $ 10,400 < y < 105,000

Regression Analysis: Justice Salary versus Court Income

The regression equation is
Justice Salary = 27.7 + 0.0373 Court Income

Predictor Coef SE Coef T P
Constant 27.701 5.519 5.02 0.002
Court Income 0.037284 0.008201 4.55 0.003

S = 12.4625 R-Sq = 74.7% R-Sq(adj) = 71.1%

Analysis of Variance

Source DF SS MS F P
Regression 1 3210.4 3210.4 20.67 0.003
Residual Error 7 1087.2 155.3
Total 8 4297.6

Predicted Values for New Observations

New Obs Fit SE Fit 99% CI 99% PI
1 57.53 5.08 (39.75, 75.31) (10.43, 104.63)

Values of Predictors for New Observations

Court
New Obs Income
1 800

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