- Recognize when a linear regression model will fit a given data set.
- Use technology to create scatterplots, find the line of best fit, and find the correlation coefficient.
- Find the estimated slope and [latex]y[/latex]-intercept for a linear regression model.
- Use the line of best fit to predict values.
Prediction and extrapolation
We can use the line of best fit to make predictions about the response variable. However, when calculating predicted values using a line of best fit, we should use it to calculate the predicted response for values of the explanatory variable within the range of values that are in the data set.
Caution: Prediction for values of the explanatory variable that fall outside the range of the data is called extrapolation. These predictions are unreliable because we do not know if the pattern observed in the data continues outside the range of the data. Avoid making predictions outside the range of the data.
Extrapolation was originally introduced when determining if it was reasonable to interpret the estimated [latex]y[/latex]-intercept. We should avoid extrapolation in practice, since it is unreliable to assume the same line will best describe the relationship between the explanatory and response variables outside the range of our data.
Let’s look at the data set about the striped ground cricket chirps and temperature!