Report the value of the adjusted multiple coefficient of determination and interpret its meaning. Test the partial regression coefficient for the variable "Performance score." Is the coefficient significant at α = 0.1? (choose your approach) Report a 99% confidence interval for the variable "Performance score." Interpret the meaning of the interval in the context of the problem. Test the partial regression coefficient for the dummy variable (β) that represents "good" treadmills. Is the coefficient significant at α = 0.1? Report a 95% interval for the mean value of all treadmills that are in "good" condition and have a performance score of 79. Interpret the meaning of the interval in the context of the problem. Report a 95% interval for the price of an individual treadmill in "good" condition with a performance score of 79. Interpret the meaning of the interval in the context of the problem. SUMMARY OUTPUT Regression Statistics Multiple R: 0.558037 R Square: 0.311406 Adjusted R Square: 0.289887 Standard Error: 718.8991 Observations: 100 ANOVA df: SS: MS: F: Significance F: Regression: 3 22437272 7479091 14.47148 7.5E-08 Residual: 96 49614328 516815.9 Total: 99 72051600 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 99.0% Upper 99.0% Intercept: -2240.44 1362.264 -1.64464 0.103314 -4944.51 463.636 -5820.49 1339.614 Performance Score: 53.72021 17.6291 3.047247 0.002983 18.72674 88.71369 7.390671 100.0498 D.Excellent: 338.0642 172.8579 1.955734 0.053404 -5.05609 681.1845 -116.209 792.3376 D. Good: -527.965 351.0141 -1.50411 0.135835 -1224.72 168.7921 -1450.44 394.5053
Added by Jessica L.
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The adjusted multiple coefficient of determination is 0.289887. This means that 28.99% of the variation in the price of treadmills can be explained by the variables included in the regression model, after adjusting for the number of variables in the model. Show more…
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SUMMARY OUTPUT Regression Statistics Multiple R R Square Adjusted R Square Standard Error 0.839168643 0.704204011 0.695504129 0.62867577 36 ANOVA df 31.9917926231.9918 80.9440875 13.43792960.39523 45.42972222 Significance F Regression Residual Total 3| 35 1.62589E-10 Coefficients Standard Error t Stat P-value 0.291093339 18.0032 5.8906E-19 0.009907724 -8.9969 1.6259E-10 Lower 95% Upper 95% Intercept 4.649041127 5.83219 Program Participation Rate (%) -0.109273652 -0.069 RESIDUAL OUTPUT Observation Predicted Nurse Attrition Rate (%) 4.340312752 4.215518525 4.43836536 4.295743385 3.974843943 3.698513867 3.734169361 3.6539445 3.440011538 3.502408652 3.520236399 3.885705208 3.181509209 3.128025969 3.092370475 3.012145614 2.985403994 2.940834627 2.700160045 2.45057159 2.654504551 2.459485463 2.388174476 2.50405483 2.200983134 2.183155387 1.995964046 1.71963397 1.817686578 1.764203337 1.66615073 1.630495236 1.487873261 1.380906781 1.318509667 1.32742354 Residuals 0.340312752 0.215518525 1.06163464 -0.595743385 -0.274843943 0.001486133 -0.234169361 0.1460555 0.059988462 0.097591348 -0.220236399 2.114294792 0.118490791 1.928025969 0.007629525 0.012145514 -0.085403994 -0.440834627 -0.200160045 0.14942841 0.164504551 -0.359485463 -0.488174476 -0.30405483 0.100983134 0.916844613 0.204035954 0.08036503 0.682313422 1.035796663 -0.16615073 -0.130495236 -0.187873261 -0.180906781 -0.218509667 0.17257646
Sri K.
Madhur L.
State the simple linear regression model. Verify manually the values of a and b given in the output: i. Provide 95% confidence intervals for a and b for the true regression model. ii. Comment on the significance of the slope parameter: Clearly justify your comment by using both the critical value and the p-value. iii. Interpret the sample correlation coefficient and the coefficient of determination; Comment on the significance of the overall regression model. Clearly justify your comment by using both the critical value and the p-value. (b) Consider the following Statistical output for multiple linear regression of literacy rate on number of newspapers, radios, and TVs (per 1000 population): Regression Summary for Dependent Variable: Literacy Rate R = 0.77978366 R-squared = 0.60806255 F-value = 5.1029 Standard Error = 0.11051 Number of Observations = 6 Intercept = 0.48888 Coefficient for Newspapers = 0.132007 Coefficient for Radios = 0.003440 Coefficient for TVs = 0.0047 Specify the multiple imputation model. Comment on the significance of the overall multiple regression model. Clearly justify your comment by using both the critical value and the p-value.
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