# Qqnormrecidualylab residualcolblue qqlinerecidual

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> qqnorm(Recidual,ylab = "Residual",col="blue") > qqline(Recidual) Interpretation: Most of the points are close to the line and the ones that a away raises a concern. > #3b > summary(lm_frig) Call:

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lm(formula = price ~ ecost + rsize + fsize + shelves + shelfsqft + features + brand) Residuals: Min 1Q Median 3Q Max -104.185 -29.875 -5.694 37.775 99.634 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) -783.325 270.741 -2.893 0.007164 ** ecost -6.453 2.262 -2.853 0.007906 ** rsize 64.094 20.263 3.163 0.003646 ** fsize 134.308 25.138 5.343 9.78e-06 *** shelves 42.001 11.308 3.714 0.000864 *** shelfsqft 3.187 7.117 0.448 0.657599 features 23.612 4.327 5.457 7.14e-06 *** brandOther 52.735 31.505 1.674 0.104907 --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 Residual standard error: 58.05 on 29 degrees of freedom Multiple R-squared: 0.8611, Adjusted R-squared: 0.8276 F-statistic: 25.68 on 7 and 29 DF, p-value: 8.37e-11 Overall F test Price = -783.325 - 6.453ecost + 64.094rsize + 134.308fsize + 42.001shelves + 3.187 shelfsqft + 23.612features + 52.735brandOther Let B’s represent the slope of the all the parameter associated with the price. Ho : B1 = B2 = B3 = B4 = B5 = B6 = B7 = 0 VS Ha : Not all the B’s are equal to Zero Alpha = any reasonable significant figure. P-value = 8.37e-11 < alpha so reject Ho. Conclution: From the out put above the F-statistic: 25.68 on 7 and 29 degrees of freedom, P-value is less than alpha to we reject null. At any significant level the data provide sufficient evidence to conclude that there is regression relation between price and predators. R a ^2 = 0.8276. Brand and features will be in the final models. R a ^2 is close to 1 indicating 82% of the variability in the price is explained by all the regression on the predators. > #4a > anova(lm_frig) 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 . features 1 98626 98626 29.2710 8.114e-06 *** brand 1 9441 9441 2.8019 0.1049066 Residuals 29 97713 3369 --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 Interpretation Extra sum of squares Ssrx1 is 191846, which is an increase in the regression sum of squares when ecost is only predator in the model. SSR(X1,X2) is an increase in the regression sum of squares when sums of squares ecost and rsize are the predator in the model. SSR(X7|X1,X2,X3,X4,X5,X6) is 9441, which is an increase sequential sums of square obtained by adding b rand in the model in which ecost, rsize, fsize, shelves, shelfsqft and features already in the model. > #4b > summary(lm(price ~ ecost + rsize + fsize + + shelves + shelfsqft + features + brand + brand*shelves)) Call: lm(formula = price ~ ecost + rsize + fsize + shelves + shelfsqft + features + brand + brand * shelves) Residuals: Min 1Q Median 3Q Max -109.660 -22.127 -3.323 32.185 120.976 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) -774.385 265.640 -2.915 0.00692 ** ecost -4.758 2.503 -1.901 0.06764 .

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