Question

Consider the following data for a dependent variable y and two independent variables, x1 and x2 30 12. 95 47 10 108 24 18 113 51 16 178 41 6 95 51 20 175 75 7 170 36 12 118 142 59 13 77 17 212 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 ai 1 Predict y if 1 = 45 b. Develop an estimated regression equation relating y to 2 2 Predict y if x2 = 25 c. Develop an estimated regression equation relating y to eı and 2 Predict y if a 45 and 2 25

Answer 1

EXCEL (Data Analysis) output:

SUMMARY OUTPUT Regression Statistics Multiple R R Square Adjusted R Square 0.600085745 Standard Error Observations 0.802820442 0.644520662 25.8518651 10 ANOVA Significance F df MS F SS Regression Residual Total 1 9693.848565 9693.849 14.50482 0.005173519 5346.551435 668.3189 15040.4 Upper 95% Coefficients Standard Error t Stat P-value Lower 95% Intercept 49.09233581 25.37977752 1.934309 0.089126 -9.433536056 107.6182077 x1 1.863699882 0.48935017 3.80852 0.005174 0.735256368 2.992143396 49.09+1.86x The estimated regression equation is

y 49.09+1.86x - 49.09+ 1.86 (45) - 49.09+83.7 -132.79 (b) EXCEL (Data Analysis) output:

SUMMARY OUTPUT Regression Statistics Multiple R R Square Adjusted R Square 0.126424559 Standard Error Observations 0.4727457 0.223488497 38.20838195 10 ANOVA Significance F df MS F SS Regression Residual Total 1 3361.356388 3361.356 2.302487 0.16764318 8 11679.04361 1459.88 9 15040.4 Coefficients Standard Error P-value Lower 95% t Stat Upper 95% Intercept x2 86.19702411 37.83407066 2.278291 0.05221 -1.048499198 173.4425474 10.4641115 4.152898923 2.736860912 1.517395 0.167643 -2.158313653 The estimated regression equation is y=86.20+ 4.15x y=86.20+4.15x 86.20+4.15(25) -86.20+103.75 =189.95

(c) EXCEL (Data Analysis) output:

SUMMARY OUTPUT Regression Statistics Multiple R R Square Adjusted R Square Standard Error 0.964317414 0.929908076 0.909881812 12.27198072 Observations 10 ANOVA Significance F 9.11671E-05 df SS MS F Regression Residual 2 13986.18942 6993.095 46.43443 7 1054.210575 150.6015 Total 15040.4 Lower 95% Coefficients Standard Error p-value t Stat Upper 95% Intercept -17.11882042 17.29063198 -0.99006 0.355124 -58.0046681 23.76702727 1.956610189 0.232947427 8.399364 6.67E-05 1.405777054 2.507443324 х1 x2 4.706050392 0.881503693 5.338662 0.001077 2.621625381 6.790475403 The estimated regression equation is -17.12+1.96x,+4.71x

17.12+1.96x+4.71x =-17.12+1.96(45)+4.71(25) - 17.12 +88.2+117.75 188.83