Transforming Nonlinear Data
Day 125 - Lesson 12.2
Use transformations involving powers and roots to find a power model that describes the relationship between two variables, and use the model to make predictions.
Use transformations involving logarithms to find a power model or an exponential model that describes the relationship between two variables, and use the model to make predictions.
Activity: How Many iPhones Will Be Sold?
Back in Section 3.2, we looked at opening weekend iPhone sales and found that a linear model for the data was not appropriate. We noticed that the residual plot showed a clear leftover curved pattern. At that point in the year, we were unable to use a model to make predictions. Today we will create a model that we can use to make predictions for the iPhone sales. We will do this by transforming the original data (using log or ln) so that it is fairly linear, then use an inverse transformation to make a prediction.
Teaching Tips for this activity:
Students will need help with #1d and #8. You will have to remind them about inverse transformations they first learned about in Algebra class. The inverse transformation for log(x) is 10 ^ (say this as "10-to-the") and the inverse transformation for ln(x) is e ^ (say this as "e-to-the").