People in real estate are interested in predicting the price of a house by the square footage, and predictions will vary based on geographic area. We look at predicting prices (in $1000s) of houses in New York state based on the size (in thousands of square feet). A random sample of 30 houses for sale in New York state is given in the dataset HomesForSaleNY. Use technology and this dataset to answer the following questions:
(a) Is square footage an effective predictor of price for houses in New York?
(b) Find a point estimate for the price of a 2000- square-foot New York home.
(c) Find and interpret a 90% confidence interval for the average price of all 2000-square-foot New York homes.
(d) Find and interpret a 90% prediction interval for the price of a specific 2000-square-foot New York home.