You have been hired by a local used car dealer to help in their pricing of used cars. (Hey, it’s temporary thing, just to help you earn some extra cash.) They want to know whether the prices of the cars they sell are more influenced by the age of the car or by the mileage on the car. (Obviously, on average, an older car has more miles on it than a newer car, but the relationship is not perfect.)

Using the data found in the Excel file, following the same steps outlined in the Lecture, run two separate regressions (one utilizing age of the car, one utilizing mileage on the car) and obtain the results table similar to the one contained in the Lecture OR similar to the one in your text found on page 127.

Interpret, in plain English, what the estimated coefficients mean for each of these regressions.

Then interpret what the R Squares mean as well. Which of the two variables, age or mileage, is a better predictor of what a car will sell for? Why?

To run two separate regressions using the data provided, you can follow these steps:

1. Open the Excel file containing the data.
2. Select the column for "Price" as the dependent variable and the column for "Age" as the independent variable for the first regression.
3. Click on the "Insert" tab, then choose "Scatter" under the "Charts" section. Select the scatterplot with smooth lines option.
4. Right-click on one of the data points in the plot and select "Add Trendline".
5. In the "Trendline Options" tab, choose the "Linear" option and check the "Display Equation on chart" box.
6. Record the coefficient and R-squared value from the equation displayed on the chart.
7. Repeat steps 2-6, but this time use the column for "Mileage" as the independent variable in the second regression.

Now, let's interpret the estimated coefficients and R-squared values for each regression:

Regression 1 (Using Age as the Independent Variable):
- The estimated coefficient for age represents the change in price for each unit increase in age. A positive coefficient indicates that as the age of the car increases, the price is expected to increase by the coefficient value.
- The R-squared value measures the proportion of the variance in price that is explained by the age of the car. A higher R-squared value indicates that age is a better predictor of car prices in this model.

Regression 2 (Using Mileage as the Independent Variable):
- The estimated coefficient for mileage represents the change in price for each unit increase in mileage. A negative coefficient suggests that as the mileage of the car increases, the price is expected to decrease by the coefficient value.
- The R-squared value measures the proportion of the variance in price that is explained by the mileage of the car. A higher R-squared value suggests that mileage is a better predictor of car prices in this model.

Comparing the two regressions, we can conclude that mileage is a better predictor of what a car will sell for based on the higher R-squared value in the regression using mileage as the independent variable. This indicates that mileage explains a greater proportion of the variation in car prices than age. However, it is also important to consider the context and limitations of the data and model used.

To analyze whether the prices of the cars are more influenced by the age or mileage, we will run two separate regressions using the data provided in the Excel file. Let's follow the following steps:

Step 1: Load the data into a statistical software tool like Excel, SPSS, or R.

Step 2: Choose the dependent variable (the variable we want to predict) which is the price of the car.

Step 3: Choose the independent variables (the factors that may influence the dependent variable) which are the age of the car and the mileage on the car.

Step 4: Run two separate regressions. In the first regression, use the age of the car as an independent variable. In the second regression, use the mileage on the car as an independent variable.

Step 5: Obtain the results table similar to the one in the Lecture or the one in your text on page 127.

Once we have the regression results, we can interpret the estimated coefficients and R-squared values.

Interpreting the estimated coefficients:

For the regression with age as the independent variable, the estimated coefficient represents the change in the price of the car associated with a one-unit increase in the age of the car. For example, if the estimated coefficient for age is -1000, it means that the price of the car decreases by $1000 for every one-year increase in the age of the car.

For the regression with mileage as the independent variable, the estimated coefficient represents the change in the price of the car associated with a one-unit increase in mileage. For example, if the estimated coefficient for mileage is -0.05, it means that the price of the car decreases by $0.05 for every one-mile increase in mileage.

Interpreting the R-squared values:

The R-squared value in a regression indicates how much of the variation in the dependent variable (price of the car) is explained by the independent variables (age or mileage). It ranges from 0 to 1, with 1 indicating a perfect fit.

A higher R-squared value suggests that the independent variable is more successful in predicting the price of the car. If the R-squared value is closer to 1, it means that the independent variable explains a larger proportion of the variation in the price.

To determine which variable, age or mileage, is a better predictor of the car's selling price, we compare the R-squared values of the two regressions. The variable associated with a higher R-squared value is considered a better predictor.

After analyzing the regression results and comparing the R-squared values, we can conclude which variable, age or mileage, is a better predictor of what a car will sell for.