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 for a certain town. All amounts are in thousands or dollars. Find the (a explained variation, (b) unexplained variation, and (c) 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. For the prediction interval, use a 99% confidence level with a court income of $800,000. a. Find the explained variation. (Round to three decimal places as needed)

Explanation / Answer

x

y

563

30

411

44

1600

92

1117

52

290

43

252

64

103

27

164

25

35

22

We use excel. First we type the values in excel. Then we go to Data and there we select Data Analysis. We input the values for Y and X and get the below output which gives us explained variation.

SUMMARY OUTPUT

Regression Statistics

Multiple R

0.79562565

R Square

0.633

Adjusted R Square

0.580594486

Standard Error

14.65743753

Observations

9

ANOVA

df

SS

MS

F

Significance F

Regression

1

2594.116676

2594.117

12.07462

0.010337844

Residual

7

1503.883324

214.8405

Total

8

4098

Coefficients

Standard Error

t Stat

P-value

Lower 95%

Upper 95%

Intercept

27.00988498

6.980337123

3.869424

0.006136

10.50401054

43.51575942

X Variable 1

0.034379501

0.009893794

3.474855

0.010338

0.010984395

0.057774606

Question a)

Answer: 0.633

x

y

563

30

411

44

1600

92

1117

52

290

43

252

64

103

27

164

25

35

22

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