1. HW 14 Key

2. 19:38 Convenience Shopping. It’s rare that you’ll find a gas station these days that only sells gas. It’s become more common to find a convenience store that also sells gas. These data describe the sales over time at a franchise outlet of a major U.S. oil company. Each row summarizes sales for one day. This particular station sells gas, and it also has a convenience store and a car wash. The column labeled Sales gives the dollar sales of the convenience store, and the column Volume gives the number of gallons of gas sold.

3. 19:38 a a.Scatterplot Sales on Volume. Does there appear to be a linear pattern that relates these two sequences? Yes, it appears to be a linear pattern.

4. 19:38 b b. Estimate the linear equation using least squares. Interpret the fitted intercept and slope. Be sure to include their units. Note if either estimate represents a large extrapolation and is consequently not reliable. As volume increases by 1 gallon, sales revenue increases.32. Fixed is 1148.

5. 19:38 c c. Interpret the summary values r squared and se associated with the fitted equation. Attach units to these summary statistics as appropriate. R squared is.42, so the model explains 42% of the variation between sales and volume.

6. 19:38 d d. Estimate the difference in sales at the convenience store (on average) between a day with 3,500 gallons sold and a day with 4,000 gallons sold. 2431-2270= 161

7. 19:38 e e. This company also operates franchises in Canada. At those operations, gas sales are tracked in liters and sales in Canadian dollars. What would your equation look like if measured in these other unites? (1 gallon=3.7854 liters and use $1=$1.1 Canadian) Include r squared and se as well as the slope and intercept. R squared remains the same because it is unitless. Intercept=1263.042 slope=1.213561

8. 19:38 f f. The form of the equation suggests that selling more gas produces increases in sales at the associated store. Does this mean that customers come to the station to buy gas and then happen to buy something at the convenience store, or might the causation work in the other direction? There is a fixed revenue of $1148 regardless of gas purchases. This would make it seem like people come to the convenience store and then happen to buy gas.

9. 19:38 g g. On one day, the station sold 4,165 gallons of gas and had sales of $1,744 at the attached convenience store. Find the residual for this case. Are these sales higher or lower than you would expect? 1,744-2484=-740 Sales are $740 less than expected.

10. 19:38 h h. Plot the residuals from this regression. If appropriate, summarize these by giving the mean and SD of the collection of residuals. What does the SD of the residuals tell you about the fit of the equation? The mean, by definition, is 0. This tells you the precision of the regression line, how close the residuals are to the regression.

11. 19:41 Seattle Homes. This data table contains the listed prices (in thousands of $) and the number of square feet for 28 homes listed by a realtor in the Seattle area.

12. 19:41 a a.Create a scatterplot for the price of the home on the number of square feet. Does the trend in the average price seem linear? A linear trend with increasing variation.

13. 19:41 b b. Estimate the linear equation using least squares. Interpret the fitted intercept and slope. Be sure to include their unites. Note if either estimate represents a large extrapolation and is consequently not reliable.

14. 19:41 c c. Interpret the summary of values r^2 and se associated with the fitted equation. Attach unites to these summary statistics as appropriate.

15. 19:41 d d. If a homeowner adds an extra room with 500 sq ft to her home, can we use this model to estimate the increase in the value of the home? 500*.147 = $73.5 thousand

16. 19:41 e e. A home with 2,690 sq ft lists for $625,000. What is the residual for this case? Is it a good deal? 625,000-469,629= $155,371 Bad deal

17. 19:41 f f. Do the residuals from this regression show patterns? Does it make sense to interpret se as the standard deviation of the errors of the fit? Use the plot of the residuals on the predictor to help decide. The variation of the residuals increases with the size of the home. A single value cannot summarize the changing variation.