AP STATISTICS Section 3.2 Least Squares Regression

Ex. Derive the LSRL for the number of TVs versus the number of rooms in someone’s house.

1. Define all variables in the model. 2. Interpret the slope and y-intercept in the context of the problem. 3. Does the y-intercept have meaning in the context of this problem? Why? 4. What is the predicted number of TVs when there are 20 rooms in a house? How do you feel about this predictions?

If most of the residuals are positive then the model is underestimating the predictions. If most of the residuals are negative then the model is overestimating the predictions. INTERPRETATION: If the residual plot is scattered, then the model is a good fit for the data. We do NOT want to see patterns in our residual plots. BEWARE: 1. A curved pattern indicates that the data is nonlinear. 2. Watch for funnel/megaphone patterns. 3. Don’t look too hard for a pattern. 4. Be careful interpreting data sets where n is small.

Ex. Use LSRL techniques to develop a model for shoe size versus height. Then calculate the residuals and create a residual plot. Data: 1. Create a scatterplot of the data. 2. Describe the scatterplot. 3. Using your calculator, derive the LSRL and find correlation. 4. How does the value for correlation support your description in #2. 5. Define all variables in the model.

6. Interpret the y-intercept in the context of the problem. Does it have meaning in this setting? 7. Interpret the slope in the context of the problem. 8. Add the LSRL to the scatterplot on your calculator. 9. What is the predicted shoe size when the height is 80 inches tall? How do you feel about this prediction? 10. Calculate the residuals for all observations. Show how the first residual was calculated.

10. Create a residual plot. 11. Interpret the residual plot.