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Analysis of Variance Table Df Sum Sq Mean Sq F value Pr(>F) plastic 1 239735 239735...

Analysis of Variance Table

Df Sum Sq Mean Sq F value Pr(>F)

plastic 1 239735 239735 241.8709 2.31e-14

paper 1 11239 11239 11.3392 0.00245

garbage 1 2888 2888 2.9136 0.10023

moisture 1 411069 411069 414.7313 2.20e-16

Residuals 25 24779 991

(a)Please calculate the MSreg and MSres. Derive the F statistic (F=MSreg/MSres)

(b) Use the F statistic to perform the overall F-test. We know that under H0, the sampling distribution of F statistic is an F distribution: F=MSreg/MSres ∼ F(p − 1, n − p), where p is the number of parameters in the multiple linear regression model and n is the sample size. Please derive the p-value: the probability that the F statistic is greater than the value we calculated in part (a). You may want to use the R code pf(y, p-1, n-p) to help you calculate the probability. With the p-value, how you can make the conclusion and what do you know about the linear model we fitted.

Math   Statistics-And-Probability   
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