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8. (6 point) An economist wants to test if there is any difference in income between Escambia county and Miami-Dade county in Florida. To do this, she collected random samples of residents from both counties. Then information collected from these samples are listed in following table : Escambia county Miami-Date county theaste 1 = 35 ng = 40 X1 = $36, 700 X2 = $34, 600 $1 = $7800 82 = $7375 Construct 95% confidence interval for the difference u.1-L129. (18 points) A study investigating the relationship between the age x (in year) and the retail value y (in thousands of dollars) of 10 randomly selected automobile of the same maker and model. The detail of data set and related result are shown below: Car 1 2 3 4 5 6 7 8 9 10 x [in yead 2 3 3 3 4 4 5 5 5 6 thpaste er ly lin thousands 28.7 24.8 26.0 30.5 23.8 24.6 23.8 20.4 21.6 22.1 of dollars) [z=40, [y= 264.3, [ 1 = 174, Cy' =6154.15, Cry = 956.5 DELLX LOB [z =40, Cy = 264.3, [ 1' = 174, Zy' = 6154.15, Cry = 956.5 la) (6 points) Find the equation of the regression line between y and x. (b) (4 points )what is expected retail value change if the age of the car in same maker and model increase by 2 years (assume it is within the sample data coverage) (c) (4 point) Use the equation in part (a) to find fitted value at x =5. theaste er (d) (4 points) Find the coefficient of determination and interpret it. (e) bonus question (5 points) Test, at 5 % level of significance, whether the age x is useful for predicting y based on the data information . Upload Choose a File