Statistics Problem.
SUMMARY OUTPUT Regression Statistics Multiple R 0.87463869 R Square 0.76499284 Adjusted R Sq 0.75916621 Standard Erro 24.4596305 Observations 125 ANOVA df SS MS F Significance F Regression 3 235646.734 78548.9115 131.292642 6.9076E-38 Residual 121 72391.0963 598.273523 Total 124 308037.831 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 90.0% Upper 90.0% Intercept 0.22140549 6.49061033 0.03411166 0.97284432 -12.62847 13.0712806 -10.537069 10.9798798 Number of Far 9.13618677 1.01756216 8.97850486 4.3514E-15 7.12165408 11.1507195 7.4495324 10.8228411 Distance from 0.88886442 0.04864591 18.2721309 1.3546E-36 0.79255702 0.98517183 0.80823167 0.96949717 Member -14.907346 4.58299617 -3.2527511 0.00148142 -23.980596 -5.8340961 -22.503865 -7.3108265SUMMARY OUTPUT Regression Statistics Multiple R 0.87463869 R Square 0.764992838 Adjusted R Sq 0.759166214 Standard Erro 24.45963048 Observations 125 ANOVA df SS MS F Significance F Regression 3 235646.7344 78548.9115 131.292642 6.9076E-38 Residual 121 72391.0963 598.273523 Total 124 308037.8307 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept 0.22140549 6.490610332 0.03411166 0.97284432 -12.62847 13.0712806 -12.62847 13.0712806 Number of Far 9.136186769 1.017562157 8.97850486 4.3514E-15 7.12165408 11.1507195 7.12165408 11.1507195 Distance from 0.888864424 0.048645909 18.2721309 1.3546E-36 0.79255702 0.98517183 0.79255702 0.98517183 Member -14.9073458 4.582996171 -3.2527511 0.00148142 -23.980596 -5.8340961 -23.980596 -5.8340961SUMMARY OUTPUT Regression Statistics Multiple R 0.87463869 R Square 0.76499284 Adjusted R Sq 0.75916621 Standard Erro 24.4596305 Observations 125 ANOVA df SS MS F Significance F Regression 3 235646.734 78548.9115 131.292642 6.9076E-38 Residual 121 72391.0963 598.273523 Total 124 308037.831 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 99.0% Upper 99.0% Intercept 0.22140549 6.49061033 0.03411166 0.97284432 -12.62847 13.0712806 -16.764991 17.2078018 Number of Far 9.13618677 1.01756216 8.97850486 4.3514E-15 7.12165408 11.1507195 6.47315307 11.7992205 Distance from 0.88886442 0.04864591 18.2721309 1.3546E-36 0.79255702 0.98517183 0.76155456 1.01617428 Member -14.907346 4.58299617 -3.2527511 0.00148142 -23.980596 -5.8340961 -26.901378 -2.91331361. The regression contains sample data on how much n=125 families spent at the Restaurant, based on the number of family members, their distance from the restaurant, and whether they had a membership or not. a. are: Run a simple linear regression with amount spent as the dependent variable and distance from the resto as the independent variable. What is the slope of your regression? What is your point estimate for how much is being spent per mile of distance? Run a multiple linear regression with amount spent as y, and family size, distance from resto and membership as your independent variables. What is your point estimate for how much is being spent per mile of distance now? Why does it differ from your answer in part why? Based on your multiple linear regression, what is the margin of error at 95% confidence for the b you estimated for distance from the resto? Based on your multiple linear regression, what is the margin of error at 90% confidence for the b you estimated for family size? Can you reject with 99% confidence the null hypothesis that the b for membership is equal to zero? Estimate how much a family of three living 50 miles from resto will spend without membership. If the annual membership costs $60, what is the minimum amount of yearly visits to the resto that would justify purchasing a yearly membership? SUMMARY OUTPUT Regression Statistics Multiple R 0.77314531 R Square 0.59775367 Adjusted R Sq 0.59448338 Standard Erro 31.7391664 Observations 125 ANOVA df SS MS F Significance F Regression 1 184130.7443 184130.744 182.782779 4.3833E-26 Residual 123 123907.0863 1007.37469 Total 124 308037.8307 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept 31.9090582 5.152448092 6.19298974 8.0991E-09 21.7101031 42.1080132 21.7101031 42.1080132 Distance from 0.85029227 0.062892751 13.5197181 4.3833E-26 0.72579992 0.97478461 0.72579992 0.97478461
