1. A student initially chooses a simple linear model (y = a + br) to understand the relationship between x and y. After she runs a linear regression analysis, she decides to try a model of the form: Which of the following best describes the reason she decided to try the nonlinear transformation of variables in the linear model? A A very low value of 2% of the linear model. B A very high value of of the linear model C A quadratic pattern in the scatter plot in the linear model D A very high p-value for the slope parameter of the linear model 2. True or false Alf a company's sales are related to their television advertisement (X1) and radio adver tisement (X2), the regression model would improve if we wld a third variable that is the sum of advertising on radio and television (X3 X1+x2) B Suppose cort (XI.X2) -0.99, then a good linear model should not include X and X2 explanatory variables at the same time C We can add an Exp(X) into the model if the residuals increase exponentially with respect to the fitted value D log Y = 8 + 8, XXy+B>X} is not a linear regression model 3. We would like to build a linear regression model for Uber to estimate the trip fare using the trip distance (positive real numbers in km) and the origin (the city is partitioned into 4 regions so that any origin belongs to one of them) (a) Write the linear regression model when the region 1 is chosen as the base category. Explain the meaning of the dummy variables. (b) We estimate the model in (a) and find the coefficients of the dummy variables for region 2 and 3 are 0.25 and 0.2 respectively. Now we build another model in which region 2 is chosen as the base category. What are the estimated coefficients of the dummy variables forrosion 1 and 3 in the new model