Question

18. Town Courts Listed below are amounts of court income and salaries paid to the town jus- tices (based on data from the Poughkeepsie Journal). All amounts are in thousands of dollars, and all of the towns are in Dutchess County, New York. For the prediction interval, use a 99% confidence level with a court income of $800,000. Court Income 65 404 1567 1131 272 252 32 111 154 Justice Salary 30 44 92 56 46 61 18 26 25

please use the equation for thr prediction invterval and not technology

Answer 1

The data can be analyzed and the result of regression and correlation can be obtained through STAT DISK as follows:

In STAT DISK just type in the data set

In STAT DISK choose ANALYSIS Correlation and Regression

Choose the level of significance the variables for which regression and correlation are to be calculated.

Click evaluate to obtain the results as follows:

Actually this software displays the output of the regression and correlation also by default so here we present the result:

Sample size n = 9

Degree of freedom = 7

Correlation Results:

Correlation coeff, r = 0.8643037

Critical r = +/- 0.666384

P-value (two-tailed) = 0.00265

Regression Results:

Y = b0 + b1:

Y intercept, b0 = 27.70148

Slope , b1 = 0.0372835

Total Variation = 4297.556

Explained variation = 3210.364

Unexplained variation = 1087.191

Standard Error = 12.46247

Coeff of Det, R^2 = 0.747021

From the output we find that the value of correlation is r = 0.8643. The data set consist of the paired set for which the regression line is given by

y = 27.70148 + 0.03728x

In the equation x represents the court income and it is the independent explanatory variable. The symbol y gives the predicted value of the justice salary for the corresponding income to the court. Here Y is the dependent otherwise the response variable which is the justice salary.

The best predicted salary for the justice when the court for the town has an income of about $800,000 is given by 57.53

When we predict the value of y variable using the x with the help of linear equation the discrepancy between the predicted between the predicted and the actual value is well explained by the regression equation. When we sum the square of all the 9 observations we obtain the explained variation.

The explained variation is the sum of the squares of the explained deviation values of all the 9 observations this value can be calculated manually but data set is available stat disk provides the output with exact value of the explained variation which is 3210.364.

When we predict the value of y variable using the x with the help of linear equation the discrepancy between the predicted and the actual value cannot be best explained by the regression lines. When we sum the square of all the 9 observations we obtain the unexplained variation.

The unexplained variation is the sum of the squares of the unexplained deviation values of all the 9 observations this value can be calculated manually but data set is available stat disk provides the output with exact value of the explained variation which is 1087.191.

The predicted interval for the using 99% confidence level with a court income of $800,000 is (10.43, 104.63). By the confident that the limit of 10.43 and 104.63 contains the salary paid to the court justice in dollars.