SUMMARY OUTPUT Regression statistics Multiple R 0.957165 0.916164 R Square Adjus
ID: 3256598 • Letter: S
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SUMMARY OUTPUT Regression statistics Multiple R 0.957165 0.916164 R Square Adjusted R Square 0.906301 Standard Error 1.493143 Observations 20 ANOVA d MS F Significance F 2 414.1844 207.0922 92.88829 7 E-10 Regression Residual 17 37.90109 2.229476 Total 19 452.0855 Coefficientsandard Err t Stat P-value Lower 95% Upper 95%ower 95.03 pper 95.0% 4.67276 0.891147 -5.24353 6.6E-05 -6.552912606 -2.7926 -6.55291 -2.7926 Intercept Package Weight 1.2924 14 0.137842 9.37606 3.95E-08 1.00159293 1.583235 1.001593 1.583235 Distance Shipped 0.036936 0.004602 8.026448 3.49 E-07 0.027226722 0.046644 0.027227 0.046644Explanation / Answer
R-squared is a statistical measure of how close the data are to the fitted regression line. It is also known as the coefficient of determination, or the coefficient of multiple determination for multiple regression.
when there is only one independent variable that is package weight
R^2 = 0.598455
59.85 % of variation is explained by the given simple linear regression model .
when we add more variables like distance shipped , we see that
R^2 = 0.91 616164 more that R^ in previous case
hence 91.6164 % of variation is explained by the given model .
R^2 increase when we add more variable,
The adjusted R-squared is a modified version of R-squared that has been adjusted for the number of predictors in the model. The adjusted R-squared increases only if the new term improves the model more than would be expected by chance. It decreases when a predictor improves the model by less than expected by chance. The adjusted R-squared can be negative, but it’s usually not. It is always lower than the R-squared.
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