Is personal spending linearly related to orders for durable goods and personal income? A recent study reported the amounts of personal spending (in trillions of dollars), amount spent on durable goods (in billions of dollars), and personal income (in trillions of dollars). A statistical package was used to fit a linear regression model, producing the output below. Source Regression Sum of Squares df Mean Square F-ratio 0.0436 2 0.0218 105 Residual 0.0019 9 0.0002 Variable Coefficient s.e. of Coeff t-ratio Constant -0.6023 0.3826 -1.57 Goods -0.0013 0.0016 -0.80 Income 0.9580 0.1023 9.36 R2 95.9% R2(adjusted) = 95.0%, s = 0.0144 with 12-3 = 9 df a) Is the regression model overall significant? Formulate the appropriate null and alternative hypotheses. Select the appropriate statistics and formulate your conclusion. b) Predict the level of personal spending when amount spent on durable goods is 130 and personal income is at 5.10. c) Use the computer output shown above to calculate 95% confidence intervals for both partial regression coefficients. Note that for 9 degrees of freedom to 025 = 2.262. d) Based on your confidence intervals in the previous question, does the amount spent on durable goods have any predictive power beyond that provided by the other independent variables for determining personal spending?