Rsize 65901 19914 3309 000258 fsize 125225 25427 4925

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rsize 65.901 19.914 3.309 0.00258 ** fsize 125.225 25.427 4.925 3.41e-05 *** shelves 14.447 21.858 0.661 0.51404 shelfsqft 1.849 7.040 0.263 0.79475 features 25.096 4.364 5.751 3.59e-06 *** brandOther -43.283 72.543 -0.597 0.55553 shelves:brandOther 35.422 24.212 1.463 0.15461 --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 Residual standard error: 56.94 on 28 degrees of freedom Multiple R-squared: 0.871, Adjusted R-squared: 0.8341 F-statistic: 23.62 on 8 and 28 DF, p-value: 1.642e-10 Let B 8 represent the slope of the interaction term shelves:brandOther parameter associated with the price. Ho : B 8 = 0 VS Ha : B 8 =/= 0 Alpha = any reasonable significant figure. P-value = 0.15461 > alpha so fail to reject Ho.
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Conclution: From the out put above the t-test is 1.463, P-value is greater than alpha so we do not reject null. At any significant level the data provide sufficient evidence to conclude that we can drop interaction terms > #4c > anova(lm(price ~ ecost + rsize + fsize + + shelves + shelfsqft + brand + features)) Analysis of Variance Table Response: price Df Sum Sq Mean Sq F value Pr(>F) ecost 1 191846 191846 56.9376 2.562e-08 *** rsize 1 30 30 0.0090 0.9252384 fsize 1 230103 230103 68.2917 4.128e-09 *** shelves 1 65418 65418 19.4154 0.0001315 *** shelfsqft 1 10305 10305 3.0584 0.0909006 . brand 1 7746 7746 2.2989 0.1402912 features 1 100321 100321 29.7740 7.137e-06 *** Residuals 29 97713 3369 --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 Let B 7 represent the slope of the predator term features parameter associated with the price. Ho : B 7 = 0 VS Ha : B 7 =/= 0 Alpha = any reasonable significant figure. P-value = 7.137e-06 < alpha so reject Ho. Conclution: From the output above the t-test is 29.7740, P-value is less than alpha so we reject null. At any significant level the data provide sufficient evidence to conclude that we cannot drop features from our model. Executive Summary The plot shows a good positive linear relation between the price and the predators. When I did not include ecost in the first backward stepwise regression, it shows that the best predator to put are fsize, rsize,
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shelves, features, brand and shelves:brand. When I did not including fsize in the second backward stepwise regression, it Shows that the best preditor to include are ecost, shelves, shelfsqft, features, brand and shelves:brand predators in our model. On the two potential model based on AIC the best predictors are ecost, fsize, shelves, features, brand and shelves:brand. Residual plot against fitted_values shows it reasonable to assume a homoscedastic because there is no regular pattern in the scattered plot. The histogra shows the residuals are left-skewed, which is problematic to make inference on this model. Most of the points on QQ-norm are close to the line and the ones that are away raises a concern. When I test the regression relation between price and predators, at any significant level the data provide sufficient evidence to conclude that there is regression relation. 82% of the variability in the price is explained by all the regression on the predators. So the best predator to include are ecost, fsize, shelves, features and brand
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