MATH
MTH4230_exam_1_review(2).pdf

# Analysis of variance table model 1 weight factorage

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Analysis of Variance Table Model 1: Weight ~ factor(Age) Model 2: Weight ~ Age Res.Df RSS Df Sum of Sq F Pr(>F) 1 40 152182 2 81 474808 -41 -322626 2.0683 0.01163 * In R I typed anova(lm(Weight factor(Age)), lm(Weight Age)) . What did I do wrong?! (d) Here is the real lack of fit test: Analysis of Variance Table Model 1: Weight ~ Age Model 2: Weight ~ factor(Age) Res.Df RSS Df Sum of Sq F Pr(>F) 1 81 474808 2 40 152182 41 322626 2.0683 0.01163 * What can you conclude from this test at a significance level of α = 0 . 05? State the null and alternative hypotheses, the p -value, your decision to reject the null or not, and your conclusion (in context). 3

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(e) Assume that the plot of weight against chest girth appears quite linear and the diagnostics confirm that the normal error SLR model is appropriate. The following shows the summary of fitting this model on these data: Call: lm(formula = Weight ~ Chest) Residuals: Min 1Q Median 3Q Max -80.000 -12.698 -3.557 13.662 93.199 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) -274.7280 13.9447 -19.70 <2e-16 *** Chest 12.8802 0.3779 34.08 <2e-16 *** --- Signif. codes: 0 *** 0.001 ** 0.01 * 0.05 . 0.1 1 Residual standard error: ***** on 81 degrees of freedom Multiple R-squared: 0.9348, Adjusted R-squared: 0.934 F-statistic: 1162 on 1 and 81 DF, p-value: < 2.2e-16 Which variable is the predictor and which is the response? Test whether chest girth and weight have a linear relationship at the α = 0 . 05 level. State the null and alternative hypotheses, the p -value, your decision to reject the null or not, and your conclusion (in context). (f) Using the output from above, fill in the missing values ( * * * * * ): > cor.test(Weight, Chest) data: Weight and Chest t = *****, df = *****, p-value < ***** alternative hypothesis: true correlation is not equal to 0 95 percent confidence interval: 0.9490929 0.9784914 sample estimates: cor ***** Is the true correlation between weight and chest girth equal to 0? State the null and alternative hypotheses, the p -value, your decision to reject the null or not, and your conclusion (in context). (g) What percent of variation in weight can be explained by the regression on chest girth?
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