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# ch11 - CHAPTER 11 Section 11-2 11-1 a yi = 0 1 xi i S xx =...

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11-1 CHAPTER 11 Section 11-2 11-1. a) i i i x y ε β β + + = 1 0 348571 . 25 42 . 157 14 43 2 = - = xx S 057143 . 59 80 . 1697 14 ) 572 ( 43 - = - = xy S ° . . . ° ° ( . )( ) . β β β 1 0 1 572 14 43 14 59 057143 25348571 2 330 2 3298017 48 013 = = - = - = - = - - = S S y x xy xx b) x y 1 0 ˆ ˆ ˆ β β + = 99 . 37 ) 3 . 4 ( 3298017 . 2 012962 . 48 ˆ = - = y c) 39 . 39 ) 7 . 3 ( 3298017 . 2 012962 . 48 ˆ = - = y d) 71 . 6 39 . 39 1 . 46 ˆ = - = - = y y e 11-2. a) i i i x y ε β β + + = 1 0 6 . 33991 8 . 143215 20 1478 2 = - = xx S 445 . 141 67 . 1083 20 ) 75 . 12 )( 1478 ( = - = xy S 32999 . 0 ) )( 0041617512 . 0 ( ˆ 00416 . 0 6 . 33991 445 . 141 ˆ 20 1478 20 75 . 12 0 1 = - = = = = β β xx xy S S x y 00416 . 0 32999 . 0 ˆ + = 00796 . 0 18 143275 . 0 2 ˆ 2 = = - = = n SS MS E E σ 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 -50 0 50 100 x y b) 6836 . 0 ) 85 ( 00416 . 0 32999 . 0 ˆ = + = y c) 7044 . 0 ) 90 ( 00416 . 0 32999 . 0 ˆ = + = y d) 00416 . 0 ˆ 1 = β

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11-2 11-3. a) ) 32 ( 0041612 . 0 3299892 . 0 ˆ 5 9 + + = x y x y x y 0074902 . 0 4631476 . 0 ˆ 1331584 . 0 0074902 . 0 3299892 . 0 ˆ + = + + = b) 00749 . 0 ˆ 1 = β 11-4. a) Regression Analysis - Linear model: Y = a+bX Dependent variable: Games Independent variable: Yards -------------------------------------------------------------------------------- Standard T Prob. Parameter Estimate Error Value Level Intercept 21.7883 2.69623 8.081 .00000 Slope -7.0251E-3 1.25965E-3 -5.57703 .00001 -------------------------------------------------------------------------------- Analysis of Variance Source Sum of Squares Df Mean Square F-Ratio Prob. Level Model 178.09231 1 178.09231 31.1032 .00001 Residual 148.87197 26 5.72585 -------------------------------------------------------------------------------- Total (Corr.) 326.96429 27 Correlation Coefficient = -0.738027 R-squared = 54.47 percent Stnd. Error of Est. = 2.39287 7258 . 5 ˆ 2 = σ If the calculations were to be done by hand use Equations (11-7) and (11-8). 3000 2500 2000 1500 10 5 0 x y S = 2.39287 R-Sq = 54.5 % R-Sq(adj) = 52.7 % y = 21.7883 - 0.0070251 x Regression Plot b) 143 . 9 ) 1800 ( 0070251 . 0 7883 . 21 ˆ = - = y c) - 0.0070251(-100) = 0.70251 games won. d) 35 . 142 0070251 . 0 1 = yds decrease required. e) 321 . 8 ) 1917 ( 0070251 . 0 7883 . 21 ˆ = - = y 679 . 1 321 . 8 10 ˆ = - = - = y y e
11-3 11-5. a) Regression Analysis - Linear model: Y = a+bX Dependent variable: SalePrice Independent variable: Taxes -------------------------------------------------------------------------------- Standard T Prob. Parameter Estimate Error Value Level Intercept 13.3202 2.57172 5.17948 .00003 Slope 3.32437 0.390276 8.518 .00000 -------------------------------------------------------------------------------- Analysis of Variance Source Sum of Squares Df Mean Square F-Ratio Prob. Level Model 636.15569 1 636.15569 72.5563 .00000 Residual 192.89056 22 8.76775 -------------------------------------------------------------------------------- Total (Corr.) 829.04625 23 Correlation Coefficient = 0.875976 R-squared = 76.73 percent Stnd. Error of Est. = 2.96104 76775 . 8 ˆ 2 = σ If the calculations were to be done by hand use Equations (11-7) and (11-8). x y 32437 . 3 3202 . 13 ˆ + = b) 253 . 38 ) 5 . 7 ( 32437 . 3 3202 . 13 ˆ = + = y c) 9273 . 32 ) 8980 . 5 ( 32437 . 3 3202 . 13 ˆ = + = y 0273 . 2 9273 . 32 9 . 30 ˆ 9273 . 32 ˆ - = - = - = = y y e y d) All the points would lie along the 45% axis line. That is, the regression model would estimate the values exactly. At this point, the graph of observed vs. predicted indicates that the simple linear regression model provides a reasonable fit to the data. 25 30 35 40 45 50 Observed 25 30 35 40 45 50 Predicted Plot of Observed values versus predicted

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11-4 11-6. a) Regression Analysis - Linear model: Y = a+bX Dependent variable: Usage Independent variable: Temperature -------------------------------------------------------------------------------- Standard T Prob. Parameter Estimate Error Value Level Intercept -6.3355 1.66765 -3.79906 .00349 Slope 9.20836 0.0337744 272.643 .00000 -------------------------------------------------------------------------------- Analysis of Variance Source Sum of Squares Df Mean Square F-Ratio Prob. Level Model 280583.12 1 280583.12 74334.4 .00000 Residual 37.746089 10 3.774609 -------------------------------------------------------------------------------- Total (Corr.) 280620.87 11 Correlation Coefficient = 0.999933 R-squared = 99.99 percent Stnd. Error of Est. = 1.94284 7746 . 3 ˆ 2 = σ If the calculations were to be done by hand use Equations (11-7) and (11-8). x y 20836 . 9 3355 . 6 ˆ + - = b) 124 . 500 ) 55 ( 20836 . 9 3355 . 6 ˆ = + - = y c) If monthly temperature increases by 1 ± F, ° y increases by 9.20836. d) 458 . 426 ) 47 ( 20836 . 9 3355 . 6 ˆ = + - = y ° . y = 426 458 618 . 1 458 . 426 84 . 424 ˆ - = - = - = y y e 11-7. a) Predictor Coef StDev T P Constant 33.535 2.614 12.83 0.000 x -0.03540 0.01663 -2.13 0.047 S = 3.660 R-Sq = 20.1% R-Sq(adj) = 15.7% Analysis of Variance Source DF SS MS F P Regression 1 60.69 60.69 4.53 0.047 Error 18 241.06 13.39 Total 19 301.75 392 . 13 ˆ 2 = σ x y 0353971 . 0 5348 . 33 ˆ - = b) 226 . 28 ) 150 ( 0353971 . 0 5348 . 33 ˆ = - = y c) 4995 . 29 ˆ = y 50048 . 1 4995 . 29 0 . 31 ˆ = - = - = y y e
11-5 11-8. a) 1050 950 850 60 50 40 x y Predictor Coef StDev T P Constant -16.509 9.843 -1.68 0.122 x 0.06936 0.01045 6.64 0.000 S = 2.706 R-Sq = 80.0% R-Sq(adj) = 78.2%

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