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4.1 Answer each of the following: a. Suppose that a simple regression has quantities N = 20, Ey=7825.94, y = 19.21, and SSR = 375.47, find R². b. Suppose that a simple regression has quantities R² = 0.7911, SST = 725.94, and N = 20, find ². c. Suppose that a simple regression has quantities Σ(y₁ - y)² = 631.63 and E= 182.85, find R². 4.2 Consider the following estimated regression equation (standard errors in parentheses): y = 64.29 +0.99x R² = 0.379 (se) (2.42) (0.18) Rewrite the estimated equation, including coefficients, standard errors, and R², that would result if a. All values of x were divided by 10 before estimation. b. All values of y were divided by 10 before estimation. c. All values of y and x were divided by 10 before estimation. 4.3 We have five observations on

4.1 Answer each of the following: a. Suppose that a simple regression has quantities N = 20, Ey=7825.94, y = 19.21, and SSR = 375.47, find R². b. Suppose that a simple regression has quantities R² = 0.7911, SST = 725.94, and N = 20, find ². c. Suppose that a simple regression has quantities Σ(y₁ - y)² = 631.63 and E= 182.85, find R². 4.2 Consider the following estimated regression equation (standard errors in parentheses): y = 64.29 +0.99x R² = 0.379 (se) (2.42) (0.18) Rewrite the estimated equation, including coefficients, standard errors, and R², that would result if a. All values of x were divided by 10 before estimation. b. All values of y were divided by 10 before estimation. c. All values of y and x were divided by 10 before estimation. 4.3 We have five observations on

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
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Please answer 4.1 and 4.2, thanks!
Qc = 2₂²/2 = exp (In(Q))e8²/2 = exp(3.717 - 1.121 x In(P)) 0.0139/2 4.7 Exercises 4.7.1 Problems 4.1 Answer each of the following: a. Suppose that a simple regression has quantities N = 20, Ey? = 7825.94, y = 19.21, and SSR = 375.47, find R². b. Suppose that a simple regression has quantities R² = 0.7911, SST = 725.94, and N = 20, find ². c. Suppose that a simple regression has quantities Σ(y₁ - y)² = = 631.63 and = 182.85, find R². 4.2 Consider the following estimated regression equation (standard errors in parentheses): y = 64.29 +0.99x R² = 0.379 (se) (2.42) (0.18) Rewrite the estimated equation, including coefficients, standard errors, and R2, that would result if a. All values of x were divided by 10 before estimation. b. All values of y were divided by 10 before estimation. c. All values of y and x were divided by 10 before estimation. 4.3 We have five observations on x and y. They are x; = 3, 2, 1,-1,0 with corresponding y values y₁ = 4,2,3,1,0. The fitted least squares line is ŷ; = 1.2 +0.8x₁, the sum of squared least squares residuals is = 3.6, (y₁ - y)² = 10. Carry out this exercise with (x₁ - x)² = 10, and a hand calculator. Compute a. the predicted value of y for xo = 4. b. the se(f) corresponding to part (a). c. a 95% prediction interval for y given xo = 4. d. a 99% prediction interval for y given xo = 4. e. a 95% prediction interval for y given x = x. Compare the width of this interval to the one computed in part (c). 4.4 The general manager of a large engineering firm wants to know whether the experience of techni- cal artists influences their work quality. A random sample of 50 artists is selected. Using years of work experience (EXPER) and a performance rating (RATING, on a 100-point scale), two models are estimated by least squares. The estimates and standard errors are as follows: Model 1: Model 2: RATING=64.289 +0.990EXPER N = 50 R² = 0.3793 (2.422) (0.183) (se) RATING= 39.464 + 15.312 ln(EXPER) N = 46 R² = 0.6414 (se) (4.198) (1.727)
Transcribed Image Text:Qc = 2₂²/2 = exp (In(Q))e8²/2 = exp(3.717 - 1.121 x In(P)) 0.0139/2 4.7 Exercises 4.7.1 Problems 4.1 Answer each of the following: a. Suppose that a simple regression has quantities N = 20, Ey? = 7825.94, y = 19.21, and SSR = 375.47, find R². b. Suppose that a simple regression has quantities R² = 0.7911, SST = 725.94, and N = 20, find ². c. Suppose that a simple regression has quantities Σ(y₁ - y)² = = 631.63 and = 182.85, find R². 4.2 Consider the following estimated regression equation (standard errors in parentheses): y = 64.29 +0.99x R² = 0.379 (se) (2.42) (0.18) Rewrite the estimated equation, including coefficients, standard errors, and R2, that would result if a. All values of x were divided by 10 before estimation. b. All values of y were divided by 10 before estimation. c. All values of y and x were divided by 10 before estimation. 4.3 We have five observations on x and y. They are x; = 3, 2, 1,-1,0 with corresponding y values y₁ = 4,2,3,1,0. The fitted least squares line is ŷ; = 1.2 +0.8x₁, the sum of squared least squares residuals is = 3.6, (y₁ - y)² = 10. Carry out this exercise with (x₁ - x)² = 10, and a hand calculator. Compute a. the predicted value of y for xo = 4. b. the se(f) corresponding to part (a). c. a 95% prediction interval for y given xo = 4. d. a 99% prediction interval for y given xo = 4. e. a 95% prediction interval for y given x = x. Compare the width of this interval to the one computed in part (c). 4.4 The general manager of a large engineering firm wants to know whether the experience of techni- cal artists influences their work quality. A random sample of 50 artists is selected. Using years of work experience (EXPER) and a performance rating (RATING, on a 100-point scale), two models are estimated by least squares. The estimates and standard errors are as follows: Model 1: Model 2: RATING=64.289 +0.990EXPER N = 50 R² = 0.3793 (2.422) (0.183) (se) RATING= 39.464 + 15.312 ln(EXPER) N = 46 R² = 0.6414 (se) (4.198) (1.727)
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