The gross state product (GSP) is the sales of all gods and services originating in a state minus the costs of any goods or services used to generate the sales. A linear regression analysis to predict GSP ($) of all 50 states of the USA was performed on the following explanatory variables: X State Average Gasoline Price (per gallon) State population size X2 X3 = State median household income (in $s) X4 = Political Party of State's Governor (1 - Democratic Party, 0 - Republican Party) (a) The table below provides partial summary information of the analysis: Source of Variation Regression Error Total DF SS 1.3065E+13 4.1834E+11 49 1.3483E+13 i. Find R and Adj-R. ii. Is the linear model significant? State appropriate hypothesis, compute the required F-Ratio and P-value, and make a conclusion. (b) The table below shows partial summary information on the slope coefficient of each variable. Coefficient SE of Coefficient VIF Predictor Constant -312779 X1 14230 X2 0.0752 X3 3.72 X4 18340 163900 88774 1.4 0.00214 1.0 1.75 1.4 32098 1.3 i. Yes or No, and Explain Why: Do the explanatory variables exhibit multicollinearity? ii. Interpret each slope coefficient. iii. Write the complete regression equation for GSP for each political party. Explain the change you find. iv. Which of the four variables are significant predictors of GSP? Make sure you write the appropriate hypotheses, compute the required P-values and then make a conclusion. (c) The residual plots are shown below. Which assumptions of linear regression are satisfied and which ones are violated? Residual Plots for State Gross State Product Frequency Percent 10 90 Normal Probability Plot -400000 -200000 200000 400000 Residual Histogram -320000 Residual Residual 400000 200000 Versus Fits 2000000 3000000 400000 1000000 Fitted Value Versus Order 200000 -160000 160000 320000 10 2025 30 35 50 Observation Order