3.The following is a plot of nitrous oxide vs average distance from major employment centers, in Boston.Note that the data is

part of the MASS library

CARRY OUT ALL HYPOTHESIS TESTING FOR THIS PROBLEM AT $\alpha=.01$.

```{r}

library(MASS)

attach(Boston)

plot(dis,nox,xlab="distance",ylab="NOx")

```

Following is the summary output after fitting a 10'th order

polynomial model.

```{r}

lm10=lm(nox~dis+I(dis^2)+I(dis^3)+I(dis^4)+I(dis^5)

+I(dis^6)+I(dis^7)+I(dis^8)+I(dis^9)+I(dis^10),data=Boston)

summary(lm10)

```

+ 3a)Based on the summary output, which is the least significant term in the regression?Is it statstically significant at level .01?

+ 3b)Fit a 9'th order polynomial model, and use the anova

command to compare the 9'th and 10'th order models with an

F test (ie anova(lm9,lm10), where lm9 is suitably defined.

Report the value of the F statistics andthe p-value? Can

the model be reduce from 10'th order to 9'th order?(ie is the p-value < .01?)

+ 3c)carry out a series of hypothesis tests for a backward

selection procedure.That is, now compare 9'th order to 8'th order, 8'th order to 7'th order, ...Proceed until you carry out a test which IS significant (ie has p-value <.01).What is the order of the polynomial model you've selected using this stepwise testing

procedure.

+ 3d)Fit all polynomial models from 1st order through 10'th order.For each model report the $R^2$ and $adjusted$ $R^2$ values.Which model maximizes $R^2$? Which model maximizes

adjusted $R^2$?