Question

eBook Video Consider the following data for a dependent variable y and two independent variables, i and 99 Round your all answers to two decimal places. Enter negative values as negative numbers, if necessary. a. Develop an estimated regression equation relating y to 21. ý= Predict y if zı = 35. b. Develop an estimated regression equation relating y to 22. + Predict y if Zz = 25. y= c. Develop an estimated regression equation relating y to %1 and 22. ỳ= + zi + Predict y if zu = 35 and 3 = 25.

Answer 1

(a) EXCEL (Data Analysis) output:

SUMMARY OUTPUT Regression Statistics Multiple R 0.810646571 R Square 0.657147863 Adjusted R Square 0.614291346 Standard Error 25.60204515 Observations 10 ANOVA df Significance F 0.004444448 Regression Residual Total 1 8 SS MS F 10050.68227 10050.68 15.33367 5243.717727 655.4647 15294.4 9 Intercept Coefficients Standard Error Stat P-value Lower 95% Upper 95% 47.53116512 25.06011222 1.896686 0.094449 -10.25755725 105.3198875 1.895282345 0.484006065 3.915824 0.004444 0.779162357 3.011402332 The estimated regression equation is û = 47.53 +1.90x -

y = 47.53 +1.90x4 = 47.53 +1.90(35) = 47.53 +66.5 = 114.03 (b) EXCEL (Data Analysis) output:

SUMMARY OUTPUT Regression Statistics Multiple R 0.475404323 R Square 0.22600927 Adjusted R Square 0.129260429 Standard Error 38.46707003 Observations 10 ANOVA df Significance F 0.164933393 Regression Residual Total 1 8 S S MSF 3456.676185 3456.676 2.336041 11837.72382 1479.715 15294.4 9 Intercept X2 Coefficients Standard Error Stat p-value Lower 95% Upper 95% 81.48449386 40.42071829 2.015909 0.078555 -11.7258496 174.6948373 4.497366881 2.942510876 1.528411 0.164933 -2.288075362 11.28280912 The estimated regression equation is û = 81.48+4.50x.

û = 81.48+4.50 x = 81.48+4.50(25) = 81.48+112.5 = 193.98 EXCEL (Data Analysis) output:

SUMMARY OUTPUT Regression Statistics Multiple R 0.972866826 R Square 0.946469861 Adjusted R Square 0.931175536 Standard Error 10.81474758 Observations 10 ANOVA Significance F 3.5489E-05 2 Regression Residual Total MS F 14475.68864 7237.844 61.88373 818.7113562 116.9588 15294.4 9 Intercept Coefficients Standard Error Stat P-value Lower 95% Upper 95% -23.96382748 15.72145994 -1.52427 0.171264 -61.13917292 13.21151796 1.990118286 0.205033082 9.706328 2.6E-05 1.505292088 2.474944485 5.102903165 0.829615321 6.150927 0.000467 3.141174657 7.064631673 The estimated regression equation is û =-23.96+1.99x + 5.10x.

V = -23.96 +1.99x4 +5.10xz =-23.96 +1.99 (35) +5.10 (25) =-23.96 +69.65 +127.5 =173.19