# Chap14_part1 - 604 Chapter 14: Multiple Regression Model...

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92 Chapter 14: Multiple Regression Model Building CHAPTER 14 14.1 (a) 17 ) 2 ( 5 . 1 ) 2 ( 3 5 5 . 1 3 5 ˆ 2 2 = + + = + + = X X Y (b) 0739 . 2 35 . 2 22 = = t t with 22 degrees of freedom. Reject H 0 . The quadratic term is significant. (c) 0739 . 2 17 . 1 22 = < = t t with 22 degrees of freedom. Do not reject H 0 . The quadratic term is not significant. (d) 5 ) 2 ( 5 . 1 ) 2 ( 3 5 5 . 1 3 5 ˆ 2 2 = + - = + - = X X Y 14.2 (a) (b) 2 0145 . 0 2717 . 1 556 . 7 ˆ X X Y - + - = (c) 52 . 18 ) 55 ( 0145 . 0 ) 55 ( 2717 . 1 556 . 7 ˆ 2 = - + - = Y (d) Based on residual analysis, there are patterns in the residuals vs. highway speed, vs. the quadratic variable (speed squared), and vs. the fitted values. (e) 39 . 3 46 . 141 25 , 2 = = F F . Reject H 0 . The overall model is significant. The p -value < 0.001. (f) 0595 . 2 63 . 16 25 - = - < - = t t . Reject H 0 . The quadratic effect is significant. The p - value < 0.001. (g) 919 . 0 2 12 . = Y r . 91.9% of the variation in miles per gallon can be explained by the quadratic relationship between miles per gallon and highway speed. (h) 912 . 0 2 = adj r 80 70 60 50 40 30 20 10 25 15 5 MPH MPG

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93 Chapter 14: Multiple Regression Model Building 14.3 (a) (b) 2 1 1 ˆ 729.8665 10.887 0.0465 Y X X = - + (c) ( 29 ( 29 2 ˆ 729.8665 10.887 79 0.0465 79 160 Y = - + = (d) There is no obvious pattern in the residual plot. (e) PHStat output: Coefficients Standard Error t Stat P-value Intercept 729.8665 169.2575176 4.312165924 0.001009972 Price (cents) -10.887 3.495239703 -3.114807831 0.008940633 Price-SQ 0.0465 0.017622784 2.638629696 0.0216284 (f) 0 2 : 0 H β = vs. 1 2 : 0 H Since the p -value = 0.0216 < 0.05, reject H 0 . There is a significant quadratic relationship between sales and price. (g) r 2 = 0.8623. 86.23% of the variation in sales can be explained by the quadratic relationship between sales and price. (h) Adjusted r 2 = 0.8393 Scatter Plot 0 20 40 60 80 100 120 140 160 180 200 0 20 40 60 80 100 120 140 Price (cents) Sales Price (cents) Residual Plot -20 -15 -10 -5 0 5 10 15 20 25 0 20 40 60 80 100 120 140 Price (cents) Residuals
Solutions to End-of-Section and Chapter Review Problems 94 14.4 (a) Scatter Diagram 0 10 20 30 40 50 60 70 0 20 40 60 80 100 120 Fertilizer Application Rate (lbs per 1000 sq. ft.) Yield (lbs) (b) 2 0041 . 0 895 . 0 643 . 6 ˆ X X Y - + = (c) 17 . 49 ) 70 ( 0041 . 0 ) 70 ( 895 . 0 643 . 6 ˆ 2 = - + = Y (d) Normal Probability Plot -5 -4 -3 -2 -1 0 1 2 3 4 5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 Z V a lue A residual analysis indicates no strong patterns. However, the distribution of residuals appears to deviate from a normal distribution according to the normal probability plot. (e) 26 . 4 32 . 157 9 , 2 = = F F . Reject H 0 . The overall model is significant. (f) The p -value < 0.001 indicates that the probability of having an F -test statistic of at least 157.32 when β 1 = 0 and β 2 = 0 is less than 0.001. (g)

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## This homework help was uploaded on 04/09/2008 for the course ENGR, STAT 320, 262, taught by Professor Harris during the Spring '08 term at Purdue University-West Lafayette.

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Chap14_part1 - 604 Chapter 14: Multiple Regression Model...

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