Q4. [30 points] The dataset \"pollution.csv\" is posted on Quercus. It contains the CO2 emission per capita (\"co2\") and GDP per capita (\"gdp\") by participating countries (\"country\"). The data were extracted from the World Bank. We are interested in studying the relationship between the CO2 emission per capita (response) and GDP per capita (predictor). In this exercise, you will use R to t the simple linear regression and to conduct the diagnostics and remedial measures. (a) [2 points] After tting the simple linear regression, plot the residuals against the tted val ues IQ. Interpret. (b) [2 points] Generate the QQ plot. Interpret. (c) [8 points] Conduct the BrownForsythe test at a = 0.05. If needed, you can use the R code in lecture 7. Use the quartiles of X to partition the dataset (resulting in 4 partitions). What do you conclude? (d) [8 points] For this question, you need to write your own program and must not use an existing package. We want to apply the Box Cox transformation as a remedial measure. Suppose Ay E {2, 1.9, 1.8, - -- ,1.8, 1.9, 2}. (i) For each value of Ay, apply the Box Cox transformation. Compute the MLE for {30 and [31, and the corresponding log-likelihood value. Present the results in a table of the following format: (ii) Plot the log-likelihood against Ay. Which Ay is the most adequate? (iii) Apply the Box Cox transformation with Ay that you picked in (ii). Fit the simple linear regression model and generate the residual plot against the tted values Y,-. Interpret. (e) [8 points] This time, apply the Box Cox transformation to the predictor and not the response. We will pick AX from {2, 1.9, 1.8, - -- ,1.8,1.9,2}. (i) For each value of AX, apply the Box Cox transformation to the predictor. Compute the MLE for [60 and ,81, and the corresponding log-likelihood value. Present the results in a table. (ii) Plot the log-likelihood against AX. Which Ax is the most adequate? (iii) Apply the Box Cox transformation to the predictor with AX that you picked in (ii). Fit the simple linear regression model and generate the residual plot against the tted values Kg. Interpret. (f) [2 points] Lastly, apply the Box Cox transformation to both the response and the predictor with: I Ay that you picked in (d) for the response 0 A X that you picked in (e) for the predictor Fit the simple linear regression model and generate the residual plot against the tted values I71. Interpret