Prepare for your exams

Study with the several resources on Docsity

Earn points to download

Earn points by helping other students or get them with a premium plan

Guidelines and tips

Prepare for your exams

Study with the several resources on Docsity

Earn points to download

Earn points by helping other students or get them with a premium plan

Community

Ask the community

Ask the community for help and clear up your study doubts

University Rankings

Discover the best universities in your country according to Docsity users

Free resources

Our save-the-student-ebooks!

Download our free guides on studying techniques, anxiety management strategies, and thesis advice from Docsity tutors

Solutions to assignment #3 questions related to simple linear regression analysis from asw textbook. Includes calculations for sum of squares, regression coefficients, and hypothesis testing.

Typology: Assignments

Pre 2010

1 / 6

Download Regression Analysis Solutions - Assignment #3 and more Assignments Introduction to Business Management in PDF only on Docsity! 1 BA 303 Assignment #3 – Solution Key Chapter 14 __ 1. ASW - page 573 - Question # 15 a. The estimated regression equation and the mean for the dependent variable are: $ . .y x yi i= + =0 2 2 6 8 The sum of squares due to error and the total sum of squares are SSE SST= ∑ − = = ∑ − =( $ ) . ( )y y y yi i i2 212 40 80 Thus, SSR = SST - SSE = 80 - 12.4 = 67.6 b. r2 = SSR/SST = 67.6/80 = .845 The least squares line provided a very good fit; 84.5% of the variability in y has been explained by the least squares line. c. r = = +. .845 9192 __ 2. ASW - page 574 - Question # 16 a. The estimated regression equation and the mean for the dependent variable are: ˆ 30.33 1.88 23.2iy x y= − = The sum of squares due to error and the total sum of squares are 2 2ˆSSE ( ) 6.33 SST ( ) 114.80i i iy y y y= ∑ − = = ∑ − = Thus, SSR = SST - SSE = 114.80 - 6.33 = 108.47 b. r2 = SSR/SST = 108.47/114.80 = .945 The least squares line provided an excellent fit; 94.5% of the variability in y has been explained by the estimated regression equation. c. r = = −. .945 9721 Note: the sign for r is negative because the slope of the estimated regression equation is negative. (b1 = -1.88) 2 __ 3. ASW - page 575 - Question # 20 a. Let x = income and y = home price. Summations needed to compute the slope and y-intercept are: 21424 2455.5 ( )( ) 4011 ( ) 1719.618i i i i ix y x x y y x xΣ = Σ = Σ − − = Σ − = 1 2 ( )( ) 4011 2.3325 1719.618( ) i i i x x y yb x x Σ − − = = = Σ − 0 1 136.4167 (2.3325)(79.1111) 48.11b y b x= − = − = − ˆ 48.11 2.3325y x= − + b. The sum of squares due to error and the total sum of squares are 2 2ˆSSE ( ) 2017.37 SST ( ) 11,373.09i i iy y y y= ∑ − = = ∑ − = Thus, SSR = SST - SSE = 11,373.09 – 2017.37 = 9355.72 r2 = SSR/SST = 9355.72/11,373.09 = .82 We see that 82% of the variability in y has been explained by the least squares line. .82 .91r = = + c. ˆ 48.11 2.3325(95) 173.5y = − + = or approximately $173,500 __ 4. ASW - page 567 - Question # 12 (this question not required – assigned in assignment #2) __ 5. ASW - page 585 - Question # 23 a. s2 = MSE = SSE / (n - 2) = 12.4 / 3 = 4.133 b. s = = =MSE 4 133 2 033. . c. 2( ) 10ix xΣ − = 1 2 2.033 0.643 10( ) b i ss x x = = = Σ − 5 F = MSR / MSE = 9836.74/310.96 = 31.63 F.05 = 5.32 (1 degree of freedom numerator and 8 denominator) Since F = 31.63 > F.05 = 5.32 we reject H0: β1 = 0. Upper support and price are related. c. r2 = SSR/SST = 9,836.74/12,324.4 = .80 The estimated regression equation provided a good fit; we should feel comfortable using the estimated regression equation to estimate the price given the upper support rating. d. ŷ = 19.93 + 31.21(4) = 144.77 __ 8. ASW - page 592 - Question # 33 a. s = 1.453 b. 23.8 ( ) 30.8ix x x= Σ − = p 2 2 p ˆ 2 ( )1 1 (3 3.8)1.453 .068 5 30.8( )y i x x s s n x x − − = + = + = Σ − $ . . . . ( ) .y x= − = − =30 33 188 30 33 188 3 24 69 $ / $y t syp p± α 2 24.69 ± 3.182 (.68) = 24.69 ± 2.16 or 22.53 to 26.85 c. 2 2 p ind 2 ( )1 1 (3 3.8)1 1.453 1 1.61 5 30.8( )i x x s s n x x − − = + + = + + = Σ − d. $ /y t sp ind± α 2 24.69 ± 3.182 (1.61) = 24.69 ± 5.12 or 19.57 to 29.81 __ 9. ASW - page 592 - Question # 35 a. s = 145.89 23.2 ( ) 0.74ix x x= Σ − = 6 p 2 2 p ˆ 2 ( )1 1 (3 3.2)145.89 68.54 6 0.74( )y i x x s s n x x − − = + = + = Σ − ˆ 1790.5 581.1 1790.5 581.1(3) 3533.8y x= + = + = $ / $y t syp p± α 2 3533.8 ± 2.776 (68.54) = 3533.8 ± 190.27 or $3343.53 to $3724.07 b. 2 2 p ind 2 ( )1 1 (3 3.2)1 145.89 1 161.19 6 0.74( )i x x s s n x x − − = + + = + + = Σ − $ /y t sp ind± α 2 3533.8 ± 2.776 (161.19) = 3533.8 ± 447.46 or $3086.34 to $3981.26