MGMT 305 Assignment 3 Gabriel Chang

Chapter 16 Exercise 1 A. Regression Statistics Multiple R 0.794631 6 R Square 0.631439 37 Adjusted R Square 0.539299 22 Standard Error 7.269276 44 Observations 6 ANOVA df SS MS F Significanc e F Regression 1 362.13048 362.1304 8 6.853031 23 0.0589334 4 Residual 4 211.36952 52.84238 Total 5 573.5 Coefficie nts Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept -6.77453 03 14.1709475 -0.47805 77 0.657562 78 -46.119388 32.57032 75 -46.11938 8 32.570327 5 x 1.229645 09 0.46971932 2.617829 49 0.058933 44 -0.0745048 2.533795 01 -0.074504 8 2.5337950 1 Regression Equation: Y = -6.7745 + 1.2296x

B. H0: There is no significant relationship between X & Y Ha: There is a significant relationship between X & Y P-value = 0.0589 > alpha = 0.05 Do not reject H0 and conclude that that there is no significant relationship between X & Y. C. Scatterplot suggests that the data is positively correlated D. SUMMARY OUTPUT Regression Statistics Multiple R 0.97201226 R Square 0.94480783 Adjusted R Square 0.90801305 Standard Error 3.24821546 Observations 6 ANOVA df SS MS F Significance F

Regression 2 541.847289 270.923644 25.6777668 0.01296631 Residual 3 31.652711 10.5509037 Total 5 573.5 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept -168.88484 39.7861933 -4.2448103 0.02394868 -295.50227 -42.267418 -295.50227 -42.267418 x 12.1870135 2.66323606 4.57601702 0.01958678 3.71140777 20.6626193 3.71140777 20.6626193 x^2 -0.1770358 0.04289548 -4.127143 0.02579792 -0.3135483 -0.0405232 -0.3135483 -0.0405232 Regression Equation: Y = -168.8848 + 12.1870x - 0.1770x 2 E. H0: Relationship between x, x 2 , and y are insignificant Ha: Relationship between x, x 2 , and y are significant T.S: F = 25.6777 P-value = 0.0129 < alpha - 0.05 Reject H0, conclude that the relationship between variables x, x 2 , and y are significant. F. Given x = 25 Y = -168.8848 + 12.1870(25) - 0.1770(25 2 ) = 25.1652

Exercise 27 A. The scatter plot approximately shows that the weight and price variables do not have a strong relationship, with many of the data points plotted in a curved line. As such, a simple linear regression model wouldn’t be appropriate. B. SUMMARY OUTPUT Regression Statistics Multiple R 0.87761985 R Square 0.77021661 Adjusted R Square 0.74149369 Standard Error 242.80435 Observations 19

ANOVA df SS MS F Significance F Regression 2 3161747.29 1580873.64 26.8153971 7.7723E-06 Residual 16 943263.237 58953.9523 Total 18 4105010.53 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept 11375.9988 2565.18531 4.43476687 0.00041612 5938.0489 16813.9488 5938.0489 16813.9488 Weight -728.33455 193.68095 -3.7604862 0.0017095 -1138.9198 -317.74928 -1138.9198 -317.74928 Weight^2 11.9737375 3.53910869 3.38326357 0.00379172 4.47116223 19.4763127 4.47116223 19.4763127 Regression Equation: Y = 11375.9988 - 728.33456x + 11.9737x 2 C. SUMMARY OUTPUT Regression Statistics Multiple R 0.84691921 R Square 0.71727214 Adjusted R Square 0.68193116 Standard Error 269.327964 Observations 19 ANOVA df SS MS F Significance F Regression 2 2944409.69 1472204.85 20.2957614 4.0827E-05 Residual 16 1160600.83 72537.5521 Total 18 4105010.53