Rent per month (dollars) 500 1000 500 1000 Size (square feet) 1500 1500 2000 2500 Stat 2 Lab #7: Regression - Prediction and Estimation Learning objectives: Describe how the regression line relates to the SD line Calculate predictions and group averages using the regression line Carry out regression calculations using the "two variable roadmap" (This problems in this lab all use the same data, a continuation from Lab #6.) 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. 1. Add the point of averages, the SD line, and the regression line to the plot. 2. Using regression, fill in the predicted rental price per month of an apartment that is 1000 square feet: $ 700 square feet: $ 1600 square feet: $ 3. To your plot in #1, add three points showing the size and predicted prices for the three apartments in #2. 4. What point on the graph shows the average price of all the 1600 square foot apartments? 5. An apartment is 2 SDs above average in both size and price. (a) Indicate where this point is on the graph. (b) Is this apartment a good deal (based only on size)? Explain why or why not. 2. Using regression, fill in the predicted rental price per month of an apartment that is 1000 square feet: $ 700 square feet: $ 1600 square feet: $ 3. To your plot in #1, add three points showing the size and predicted prices for the three apartments in #2. 4. What point on the graph shows the average price of all the 1600 square foot apartments? 5. An apartment is 2 SDs above average in both size and price. (a) Indicate where this point is on the graph. (b) Is this apartment a good deal (based only on size)? Explain why or why not. 6. An apartment is selected at random. It is 1252.5 square feet in area, which means that it SD(s) above the average size among all the apartments being studied. is Another way of expressing the relative size of this apartment is that it is at the percentile among all apartments. 7. Using regression, we can predict the apartment from #6 will have a rental price that is SD(s) above average. Expressed as a dollar amount, this is $ Expressed as a percentile rank, this is the percentile of all the rental prices. Note: If you did #6 and #7 correctly, the percentile predicted percentile rank for price has moved closer to the median (50th percentile) than the percentile rank for area was. This is an example of the regression effect.