3. Hyundai has hired you as an analyst to help them plan their production of their different car models. They have specifically asked you to build a model to predict monthly sales of one of Hyundai's car models, the Elantra. The dependent variable is: 2 . Sales: the sales of the Elantra in the US in a given month in some historical period. The independent variables are: . Unemployment: the unemployment rate (in %) in the US in a given month. . Queries: a measure of how many queries are executed on Google for "hyundai elantra" in a given month. . CPI . Energy: the consumer price index for energy; a metric of how much energy (e.g., gasoline, electricity, etc.) costs for consumers in a given month. . CPI . All: the consumer price index for all product; a metric of the overall price of all products and services cost for consumers in a given month. The data is provided in the CSV file elantra. csv. Load the data by running the following command in R: elantra. df = read. csv("elantra. csv") Then, run a linear regression and inspect the linear regression model using the following command: elantra. Im = 1m(Sales ~ Unemployment + Queries + CPI . Energy + CPI . All, data = elantra. df) summary (elantra . Im) (a) Based on the output from the summary command, write down the regression equation. (b) Which variables are statistically significant at the o = 0.05 significance level? (c) What fraction of the variation in Sales is explained by this regression model? (d) For a particular month, Hyundai anticipates Unemployment will be 10.0, Queries will be 140, CPI . Energy will be 200, and CPI . All will be 200. Find the predicted number of sales and a 90% prediction interval for the actual number of sales. (e) The variable CPI. All is a metric of the overall price of all products purchased by consumers in the United States. The higher CPI. All is, the more consumers tend to be paying for product- s/services. As such, it stands to reason that an increase in CPI.All should lead to a decrease in Sales, yet the coefficient for CPI . All is positive (i.e., as CPI . All increases, we predict Sales to increase as well). How do you explain this contradiction? To improve your model, you now consider adding Month as an independent variable. Your rationale for including the month is that you believe there may be some seasonality in car sales, with some months being associated with higher sales and some being associated with lower sales. Run the following two commands in R: elantra. Im. 2 = 1m(Sales ~ Unemployment + Queries + CPI . Energy + CPI . All + Month, data = elantra. df) summary (elantra . Im. 2) 3 (e) Explain why this new model may not be the best way to account for seasonality. (Hint 1: What does the slope of Month mean? Hint 2: Suppose that you believe sales generally increase from January to March, and then decline from July to October. Is it possible to choose a slope for Month that would allow you to model this?) To allow the model to account for seasonality more generally, you consider converting Month to a factor or categorical variable. Run the commands below in R, which will create a new factor variable MonthFactor), and run the linear regression: elantra. df$MonthFactor = as . factor (elantra. df$Month) elantra. Im. 3 = Im(Sales ~ Unemployment + Queries + CPI . Energy + CPI . All + MonthFactor, data = elantra. df) summary (elantra . Im. 3) (f) Interpret the intercept of this model. (g) Interpret the slope of MonthFactor7. (h) Is this a better model than the one in parts (a) - (e) (elantra. Im. 1)? Explain your