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Problem 2. In this problem and the next, we'll use data of used cars listed for sale at to build regression models for predicting used car prices. a. Read the used car listing data into R. Extract all the listings for a used Honda Accord. Using the extracted data, build a regression to predict the price of a used Honda Accord (Yprice) based on its mileage (xmileage). That is, fit the model Yprice = Bo + B1 xmileage + € on the Accord data. What is the value of each coefficient Bo,B1? Comment on your interpretation of these values. How well does the model fit the data (i.e., what is the R² and RMSE)? b. Given a used Honda Accord with an odometer reading of 50,000 miles, compute the model estimated mean price, confidence interval for that mean, and the prediction interval of the price (You can use the predict. Im function in R). Compute the model estimated mean price for a Honda Accord with an odometer reading of 300,000 miles. Based on the two results, what is a critical issue in your current regression model? C. How would you address the critical issue identified in the previous section? Update your regression model by implementing your recommendation. d. Graphically present your regression models from part (a) and part (c). Specifically, plot the data with a scatter plot, and include two regression lines (with the corresponding confidence bands), one for each of the models above. Note that this can be easily achieved in R using ggplot2 with geom_smooth. For example, the model from part (a) can be plotted with ggplot (data, aes (x=mileage, y=price) ) + geom_point() + geom_smooth(method="lm", formula = y - x) - Problem 3. Continuing from the previous problem, we will further investigate the regression model for predicting used car prices. a. Refine your regression model from Problem 2-c to include the model year as a predictor (still using only the Honda Accord data). Compare the R² and RMSE of the revised regression model to your original one (i.e., the one in 2-c). b. Now, fit your model from above (Problem 3-a) on the entire dataset, instead of just on the extracted Accord data. Compare the R² and RMSE between the two models. What is the major issue in the new model? C. Update the model from Problem 3-b to address the major issue discovered. Compute the R² and RMSE of the updated model. Briefly discuss your findings. Prepare a short report detailing your results. Please submit the following: (1) your report as a single PDF file; and (2) a single, fully functional R script or markdown file that we can run to reproduce all the numerical results and plots in your report. We will put the necessary data file (used_cars_clean.tsv) into the same directory as your script before running it.

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