1. Prediction of diamond price

set.seed(1)data(diamonds)diamonds size=5000)

1. Use thesummary()function to obtain summaries of each variable in the diamonds dataset. How many categorical variables are there? How many quantitative variables? Are there any missing values?
2. Use thextabs()function to obtain cross-tabulations of all possible pairs of categorical variables. How many diamonds are of the best cut (Ideal) and clarity (IF)?
3. Excluding price (our response variable), which three quantitative variables are most highly correlated with carat (weight of the diamond)?
4. Remove x, y and z from the dataset and fit a model with price as the response variable and all main effects and possible interactions as explanatory variables. Call your fitted modelfit.full.
5. Starting fromfit.full, and using the null model as the smallest model, use stepwise selection to select a model, using the BIC criterion. (You don't need to specify thescopeof the models -step()will search fromfit.fullto the null model by default.) What main effects and what interactions are included in the final model?
6. For eachcategoricalexplanatory variable that appears in an interaction with carat in the model selected by stepwise selection, produce a scatterplot of price versus carat with the categorical interaction variable as color. For example, if there is a carat:clarity interaction, do