A realtor collects data about the rental prices of apartments in a neighborhood and their size measured in square feet. They find that the apartments have an average size of 1000 square feet, with a standard deviation of 300 square feet. The apartments have an average rental price of $1500 per month, with a standard deviation of $400. The two variables have a correlation of r = 0.5. A scatterplot of the two variables looks football shaped.

1. Recall that last time we found the following predictions of price based on size:

1000 square feet: predicted price = $1500

700 square feet: predicted price = $1300

1600 square feet: predicted price = $1900

The above predictions all are subject to error. The average size of such errors is about $___16.66%_____, and 95% of the predictions we make using regression will be correct to within about $__1140________. If we predicted rental price without taking size into account, the average size of the errors would be $__650___, and 95% of the predictions we make using regression will be correct to within about $___712.5___.

Answer the following question:

2. An apartment is at the 25th percentile in terms of area. Use regression to predict what its percentile rank will be in terms of price. (Hint: This is similar to what you did in #6 and #7 in the last lab, but starting with percentile rank for x rather than x in original units, and without prompting you for the intermediate steps. Look at the roadmap.)