Note: There are often multiple ways to answer each question.
Install and load the caret package. Also load the ggplot2 and dplyr packages. Load the Sacramento dataset with data(Sacramento). Plot a histogram of the house prices with 50 bins.
Make a violin plot of price for each level of type. Overlay this with a scatterplot with the same x and y aesthetics, but define the col by factor(beds) and introduce jitter and alpha for the points. Make some observations.
Do a \(t\)-test at the 95% level to see if the mean price for multi-family homes is statistically different from that for residential homes. (The test should be two-sided.)
Instead of doing a \(t\)-test, do a Kolmogorov-Smirnov test at the 95% level to see if the distribution of multi-family homes is statistically different from that for residential homes. (Again, the test should be two-sided.)
Make a boxplot of price for each level of beds. Make another boxplot of price for each level of baths. Do you see a trend? (Note: You will want to plot factor(beds) and factor(baths), as plotting separate boxplots for different values of a numeric variable doesn’t work.)
Fit an additive linear model of price against beds and baths with no interaction term. Interpret the coefficients of the model.
Instead of fitting an additive linear model of price against beds and baths with no interaction term (as in Question 6), fit a linear model as above but with an interaction term.
Drop the columns zip, latitude and longitude from the dataset and save the result to df.
We have many more columns of information in our dataset df that could help to predict price. Fit an additive linear model (with no interaction terms) of price against all other columns in df. (You will have to google around to find out how to do this!)
Make a scatterplot of price against sqft and include the linear model fit on the plot (without standard error intervals). Make the title and axis labels informative. Fit the model as well and look at the R-squared value (how well sqft predicts price).
Get the median house price for each city. Plot it on a map, with each city depicted by a point whose size is determined by the number of houses, and color determined by the median price.