**Lesson 2.7 – Assessing a Regression Model**

**Use a residual plot to determine if a regression model is appropriate.****Interpret the standard deviation of the residuals.****Interpret***r*².

**Activity: How many iPhones will sell?**

For this Activity, we took some data from a Yummymath activity because we wanted something relevant and non-linear. Students quickly recognized the data as nonlinear. They tried fitting a line and then a quadratic. The quadratic model fit the data the best and it showed a residual plot with no leftover pattern.

We tried to relate s (standard deviation of the residuals) back to the scatterplot and the residual plot by recognizing that essentially s is telling us the average distance that each point is away from the model in the scatterplot or how far each residual is away from the x-axis. We like the use of “typically varies” in the interpretation in the text because it is consistent with the interpretation of standard deviation from Lesson 1.7 (after all, s is a standard deviation).

**Notes**

Students struggled with the interpretation of r^{2} even after we looked at the discussion of the sum of squares in the text. We settled on a much simpler (and less statistically sound) version: “The LSRL improves our predictions for y by ____%”.

It is important that students use precise statistical language when trying to choose the best model for a set of data. All too often, students say “**it** is quadratic because **it** shows no pattern”. “it” is so vague and needs to be clarified by saying “**the scatterplot** of Iphone sales versus year is quadratic because the **residual plot** shows no pattern. Students should know the distinction between scatterplot and residual plot. We are trying to find a model for the scatterplot. The residual plot tells us whether or not our model is a good one.