Court_Income Justice_Salary61 27408 431569 901135 58260 45252 62103 25169 2326 24 Listed below are amounts of court income and salaries paid to the town justices for a certain town. All 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 aclaim 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 $800,000.Court IncomeJustice Salarya. Find the explained variation.(Round to three decimal places as needed.)b. Find the unexplained variation.(Round to three decimal places as needed.)c. Find the indicated prediction interval.$

Given Information: The amount of court income and salaries paid to the town justice are given. The sample size, n=9. To determine the explained variation, unexplained variation, and prediction interval.(a) Let x be the independent variable that denotes the court income and y be the dependent variable that denotes the justice salary, The following table shows the values of x-x¯2, y-y¯2, and x-x¯y-y¯. S.No. x y x-x¯ x-x¯2 y-y¯ y-y¯2 x-x¯y-y¯ 1 61 27 -381.556 145584.6 -17.1111 292.7901 6528.84 2 408 43 -34.5556 1194.086 -1.11111 1.234568 38.39506 3 1569 90 1126.444 1268877 45.88889 2105.79 51691.28 4 1135 58 692.4444 479479.3 13.88889 192.9012 9617.284 5 260 45 -182.556 33326.53 0.888889 0.790123 -162.272 6 252 62 -190.556 36311.42 17.88889 320.0123 -3408.83 7 103 25 -339.556 115298 -19.1111 365.2346 6489.284 8 169 23 -273.556 74832.64 -21.1111 445.679 5775.062 9 26 24 -416.556 173518.5 -20.1111 404.4568 8377.395 Total 3983 397 0 SSxx=2328422 SSyy=4128.889 SSxy=84946.44 Mean x¯=442.5556 y¯=44.11111 The value of the explained variation will be calculated as: R2=SSxy2SSxx×SSyy=84946.4422328422×4128.889=0.750 Thus, the explained variation is 0.750.(b) The value of the unexplained variation will be calculated by the formula given below: Unexplained variation = 1- Explained variation=1-R2=1-0.750=0.250 So, the unexplained variation is 0.250. (c) Now, the slope of the regression line y=a+bx will be computed as: b=SSxySSxx=84946.442328422=0.036482 The intercept of the regression line will be: a=y¯-bx¯=44.11111-0.036482×442.5556=44.11111-16.1453=27.965 The regression line will be: y=27.965+0.036482xThe predicted value when the court income is 800 will be calculated by putting x=800 in the above regression line. y'=27.965+0.036482×800=27.964+29.1856=57.15 The standard error for the predicted value is: Se=y-y'2n-2=27-57.152+...+24-57.1529-2=808.48=28.43 Now, the standard predicted error value will be determined as: Spred=Se1+1n+x-x¯2SSxx=28.431+19+800-442.555622328422=28.43×1.08=30.70 The degree of freedom will be: df=n-2=9-2=7 Using excel, the t-critical value for 0.01 level of significance and 7 degree of freedom will be:The 99% predicted interval will be computed as: P.I.=y^±t×Spred=57.76±3.499×30.70=57.76±107.43= 49.67,165.2 Therefore, the 99% predicted interval with a court income of $800 is $49.67,$165.2.