STAT 269 - Introductory Statistics
Regression and Correlation Examples
A realtor in a suburban area would like to be able to estimate the price of a house based on the square feet
of living area, so that home buyers have a rough idea of what they may be able to afford. She randomly
selects eight currently listed houses, and obtains the square feet of living space, and the asking price. The
table below displays the data in hundreds of square feet, and thousands of dollars.
Living Space 15 38 23 16 16 13 20 24
Selling Price 145 228 150 130 160 114 142 265
The summary values for this data set are:
Sxx = 451.875 Syy = 18949.5Sxy = 2097.25
•Find the correlation, and fit a regression line to the data.
•Given the following (using a 0.05 level test) would you conclude that the amount of living space a
house has helps to predict the selling price?
3. Rejection Region: Reject H0if T S > 5.9874
4. Test Statistic: T S = 6.337
5. P-value: P= 0.045
The Quick Sell car dealership has been using 1-minute spot ads on a local TV station. The ads always
occur during the evening hours and advertise the different models and price ranges of cars on the lot that
week. During a 10-week period, the Quick Sell dealer kept a weekly record of the number of TV ads versus
the number of cars sold. The results are given in the following table.
Ads Bought 6 20 0 14 25 16 28 18 10 8
Cars Sold 15 31 10 16 28 20 40 25 12 15
The summary values for this data set are:
Sxx = 682.5Syy = 825.6Sxy = 690.0
•Find the correlation, and fit a regression line to the data.
•Given the following (using a 0.01 level test) would you conclude that the number of ads bought helps
to predict the number of cars sold? Also, if the manager decides that they can only afford 12 spots
per week, predict the number of cars they should expect to sell in an average week.
3. Rejection Region: Reject H0if T S > 11.2586
4. Test Statistic: T S = 43.60
5. P-value: P≈0