## James P. Dildine Email Lisa Silver Email

Welcome to the ARPE Mini-Module! This activity is a day lesson that explores real data through graphing the scatterplot and determining the regression line. Please contact us both via email.

We encourage you to look at the full module as time allows.

First, you will need to Download the excel file. The data are about cars repaired at the Technology Center of DuPage.

The X values represent the age of the car and the Y values represent the mileage.

Sketch the scatterplot of the dataset. When one of the variables influences or helps explain the other, always plot this, called the independent variable, on the horizontal axis (the X-axis) of a scatterplot. Notice car age helps to explain car mileage so it is the independent variable and plotted along the horizontal axis. Car mileage is the dependent variable and plotted on the vertical axis. What does that mean? Give another that has dependent and independent variables.

Your scatterplot should look similar to the graph shown on the Excel file. What does one point on the scatterplot represent? All of the points demonstate the relationship of one variable with another. In other words the graph shows how car age helps to determine car mileage. What would you expect the relationship of car age to mileage to be, a positive or negative association? Explain.

The regression line explains how the dependent variable Y (car mileage) changes with independent variable X (car age). This line is often used to predict the value for Y for a given X. Each point changes the regression equation. Let's say a car came into the TCD to be repaired. The car is 3 years old with 40,000 miles. Add this point to the dataset and note the change in the regression line. Add a few more cars and explain what happens to the regression line as data are added.

How good of a prediction can you make for y based on the value of X? r2 is a measure of how successful the regression equation is in explaining the dependent variable. r2 ranges from 0 to 1. For instance, from this dataset (before entering new values) r2 = 0.1205. This means that approximately 12% of the dependent variable, car mileage, is explained by the age of the car. There are other factors, or variables, that contribute the other 88% explanation of the car's mileage. What are some variables that you can think of that would help explain a car's mileage? Notice that as you add car's repaired the r2 value changes. Try to make the r2 as high and as low as possible. Explain what you had to do to accomplish both goals.

What other information could you ask the technicians at TCD to collect in order to help explain the car mileage further? Detail another dataset that you could collect, graph the scatterplot, and regression line. What would be the dependent and independent variables? How would you collect the data?  Do you expect the relationship to be positively or negatively associated?