In an earlier assignment, you saw that you could calculate what is called the correlation coefficient when you have data for two quantitative variables to see if those variables might have a linear relationship. If the variables do have a linear relationship, the next step is to create what you call the regression line. You have seen that when you have data for two quantitative variables, you are able to create a scatterplot of the data. A regression line is simply a straight line that comes closest to the points in the scatterplot. To create the equation for the regression line, you just need to know how to get what is called the slope and the y-intercept.
- Answer the following questions in a Word document:
- Given the following data where city MPG is the response variable and weight is the explanatory variable, explain why a regression line would be appropriate to analyze the relationship between these variables:
Mazda MX-5 Miata
- Construct the regression line for this data.
- Interpret the meaning of the y-intercept and the slope within this scenario.
- What would you predict the city MPG to be for a car that weighs 3000 pounds?
- If a car that weighs 3000 pounds actually gets 32 MPG, would this be unusual? Calculate the residual and talk about what that value represents.