Part B $$ Using an Interaction plot $$ Antidotes for toxins

This problem is based on an exercise from page $134$ of the textbook, $$Modern Statistics for the Life Sciences$$

An experiment was conducted on the effectiveness of two antidotes to four different doses of toxin. The antidote was given five$-$minutes after the toxin, and twenty$-$five minutes later the response was measured as the concentration of related products in the blood. There were three subjects at each combination of the antidote and dose level. The data are stored in the dataset antidotes. Answer the questions that follow.

To load the dataset, first change working directories, and then read in the dataset:

antidotes $<-$ read.table$("$antidotes$.$txt$",$header$=$T$)$

Now antidotes contains three vectors: BLOOD, DOSE, and ANTIDOTE.

Column Descriptions of each column Name of each column in R

$1$ Antidote type $(1$ for Antidote A$,2$ for Antidote B$)$ ANTIDOTE

$2$ Four levels of dose $(5,10,15,$ and $20)$ DOSE

$3$ Concentration of products in the blood BLOOD

First do the following:

attach$($antidotes$)$

ANTIDOTE $<-$ factor$($ANTIDOTE$)$

DOSE $<-$ factor$($DOSE$)$

$1.$ Explain why we apply the function, factor$(),$ to the ANTIDOTE and DOSE variables.

$2.$ Build a linear model for the response variable including both explanatory variables, ANTIDOTE and DOSE, with and without the interaction term ANTIDOTE:DOSE.

model$1<-$lm$($BLOOD~ANTIDOTE$+$DOSE$)$

model$2<-$lm$($BLOOD~ANTIDOTE$+$DOSE$+$DOSE:ANTIDOTE$)$

Insert copies of the anova and summary tables for the model without interactions here:

Insert copies of the anova and summary tables for the model with interactions here:

$3.$ Create an interaction plot for this data using the interaction.plot$()$ command, and insert that plot right after this step.

Insert a copy of your interaction plot here, along with the command you ran in R to generate it:

$4.$ Is it important to include the interaction term for this analysis?

a$.$ Answer based on interpreting the results from the interaction plot.

b$.$ Answer based on the statistical significance of the interaction term.

$5.$ Finally, compare the multiple R$2$ result for the models without and with the interaction term.

R$2$ for model without interactions:

R$2$ for model with interactions:

Which model explains more of the variation in the data?