Solution to Tutorial 4 - Solutions to Tutorial 4 1. An...

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Solutions to Tutorial 4 1. An output of a simple linear regression model Y i = β 0 + β 1 X i + ε i ,i =1 , .., 10 is as follows Coefficients: Estimate Std. Error t value P-value (Intercept) -0.07727 0.12005 -0.644 0.537814 x 0.97295 0.14345 6.783 0.000140 Residual standard error: 0.3761 on 8 degrees of freedom Multiple R-squared: 0.8519, Adjusted R-squared: 0.8333 F-statistic: 46 on 1 and 8 DF, p-value: 0.0001403 (a) b 0 = 0 . 07727 ,b 1 =0 . 97295 ,s ( b 0 )=0 . 12005 ( b 1 . 14345 ,t ( b 0 )= 0 . 644 , t ( b 1 )=6 . 783 ,R 2 . 8519 , ˆ σ . 3761 ,r XY =+ R 2 0 . 8519 , F-statistic=46 (b) SSE . 3761 2 8=1 . 131610; SST = SSE/ (1 R 2 )=7 . 640849; SSR = =6 . 509239 Source SS DF MS F-vale regression 6.509239 1 6.509239 46.01756 error 1.131610 8 0.1414512 Total 7.640849 9 (c) t = ± ± ± 0 . 97295 1 0 . 14345 ± ± ± . 1885674 <t (1 0 . 05 / 2 , 8) = 2 . 306 we accept H 0 2. Sales Growth (R code) i 1 23456789 1 0 X i : Y e a r 0 123456789 Y i : Sales 98 135 162 178 221 232 283 300 374 395 (a) There is nonlinear pattern; see the ±rst panel in Figure 1 (b) ˆ z = 10.26 + 1.07 x (SE) (0.2129) (0.0399) 1
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(c) Does the regression line appear to be good to the transformed data? Answer: YES (for the transformed data); See the second panel in Figure 1 (d) See the thrid and 4th panels in Figure 1 below. 02468 100 200 300 400 x y 10 12 14 16 18 20 x z -0.4 0.0 0.2 0.4 x residuals Histogram of residuals residuals
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This note was uploaded on 10/04/2010 for the course STAT ST3131 taught by Professor Xiayingcun during the Fall '09 term at National University of Singapore.

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Solution to Tutorial 4 - Solutions to Tutorial 4 1. An...

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