mont4e_sm_ch11_sec02 - CHAPTER 11 Section 11-2 11-1 a) y i...

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11-1 CHAPTER 11 Section 11-2 11-1 a) i i i x y ε β + + = 1 0 348571 . 25 42 . 157 14 43 2 = = xx S 057143 . 59 80 . 1697 14 ) 572 ( 43 = = xy S ± . . . ±± (. ) () . β ββ 1 01 572 14 43 14 59 057143 25348571 2 330 2 3298017 48 013 == =− = −− = S S yx xy xx 123 . 22 59143 . 137 71429 . 159 59 . 137 ) 057143 . 59 ( 3298017 . 2 ˆ 1 = = = = = = R yy E xy R SS S SS S SS 8436 1 12 123 22 2 2 . . n SS MS ˆ E E = = = = σ b) x y 1 0 ˆ ˆ ˆ + = 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 + + = 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 = = = = = 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
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11-2 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 11-3 a) The regression equation is Rating Pts = - 5.56 + 12.7 Yds per Att Predictor Coef SE Coef T P Constant -5.558 9.159 -0.61 0.549 Yds per Att 12.652 1.243 10.18 0.000 S = 5.71252 R-Sq = 78.7% R-Sq(adj) = 78.0% Analysis of Variance Source DF SS MS F P Regression 1 3378.5 3378.5 103.53 0.000 Residual Error 28 913.7 32.6 Total 29 4292.2 i i i x y ε + + = 1 0 106 . 21 30 ) 55 . 219 ( 847 . 1627 2 = = xx S 037 . 267 30 ) 2611 )( 55 . 219 ( 21 . 19375 = = xy S 56 . 5 30 55 . 219 ) 652 . 12 ( 30 2611 ˆ 652 . 12 106 . 21 037 . 267 ˆ 0 1 = = = = = xx xy S S x y 652 . 12 56 . 5 ˆ + = 6 . 32 28 7 . 913 2 ˆ 2 = = = = n SS MS E E σ
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11-3 Yds per Att Rating Pts 9 8 7 6 5 120 110 100 90 80 70 60 S 5.71252 R-Sq 78.7% R-Sq(adj) 78.0% Fitted Line Plot Rating Pts = - 5.558 + 12.65 Yds per Att b) 33 . 89 ) 5 . 7 ( 652 . 12 56 . 5 ˆ = + = y c) 652 . 12 ˆ 1 = β d) 79 . 0 10 652 . 12 1 = × e) 66 . 85 ) 21 . 7 ( 652 . 12 56 . 5 ˆ = + = y 56 . 7 66 . 85 1 . 78 ˆ = = = y y e 11-4 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
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11-4 d) All the points would lie along a 45 degree 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
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mont4e_sm_ch11_sec02 - CHAPTER 11 Section 11-2 11-1 a) y i...

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