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ECO578 Final Exam Spring 2016 A++
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Using the “eyeball” method, the regression line y ̂ = 2+2x has been fitted to the data points (x = 2, y = 1), (x = 3, y = 8), and (x = 4, y = 7). The sum of the squared residuals will be 7 b. 19 c. 34 d. 8 A computer statistical package has included the following quantities in its output: SST = 50, SSR = 35, and SSE = 15. How much of the variation in y is explained by the regression equation? 49% b. 70% c. 35% d. 15% In testing the significance of b, the null hypothesis is generally that β = b b. β ≠ 0 c. β = 0 d. β = r Testing whether the slope of the population regression line could be zero is equivalent to testing whether the population _____________ could be zero. standard error of estimate c. y-intercept prediction interval d. coefficient of correlation A multiple regression equation includes 4 independent variables, and the coefficient of multiple determination is 0.64. How much of the variation in y is explained by the regression equation? 80% b. 16% c. 32% d. 64% A multiple regression analysis results in the following values for the sum-of-squares terms: SST = 50.0, SSR = 35.0, and SSE = 15.0. The coefficient of multiple determination will be R^2= 0.35 b. R^2= 0.30 c. R^2= 0.70 d. R^2= 0.50 In testing the overall significance of a multiple regression equation in which there are three independent variables, the null hypothesis is H_(0 ): β_1= β_2= β_3=0 H_(0 ): β_1≠ β_2 and β_2 ≠β_3 H_(0 ): β_1= β_2=β_3=1 H_(0 ): β_1= β_2=β_3=α In a multiple regression analysis involving 25 data points and 4 independent variables, the sum-of-squares terms are calculated as SSR = 120, SSE = 80, and SST = 200. In testing the overall significance of the regression equation, the calculated value of the test statistic will be F = 1.5 c. F = 5.5 F = 2.5 d. F = 7.5 For a set of 15 data points, a computer statistical package has found the multiple regression equation to be y ̂ = -23 + 20x_1+ 5x_2 + 25x_3 and has listed the t-ratio for testing the significance of each partial regression coefficient. Using the 0.05 level in testing whether b_1= 20 differs significantly from zero, the critical t values will be t = -1.960 and t= +1.960 t = -2.132 and t = +2.132 t = -2.201 and t = +2.201 t = -1.796 and t = +1.796 Computer analyses typically provide a p-Value for each partial regression coefficient. In the case of b_1, this is the probability that β_1 = 0 b_1 = β_1 the absolute value of b_1could be this large if β_1= 0 the absolute value of b_1could be this large if β_1≥ 1 In the multiple regression equation, y ̂ = 20,000 + 0.05x_1+ 4500x_2 , y ̂ is the estimated household income, x_1 is the amount of life insurance held by the head of the household, and x_2 is a dummy variable (x_2 = 1 if the family owns mutual funds, 0 if it doesn’t). The interpretation of b_2 = 4500 is that owing mutual funds increases the estimated income by $4500 the average value of a mutual funds portfolio is $4500 45% of the persons in the sample own mutual funds the sample size must have been at least n = 4500
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