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. A0ll amounts are in thousands of 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

Solution:-

Explained variation

This is the amount that other variables in the data set explain differences between the values of the variable.

Unexplained variation

Some differences between the values cannot be explained in terms of the changing values of other variables in the data set.

Formula:

Correlation Coefficient ( r ) = N x XY - ( X ) ( Y ) / N x ( X2 - ( X )2 N x ( Y2 - ( Y )2

Coefficient of Determination ( r2 ) = r x r.

The explained variable is R2 = 0.80986

The unexplained variable = 1 - R2 = 1 - 0.80986 = 0.19014

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