Question4 (30 points) A research to study the amount of the GAS fuel a 4x 4 car uses, given the running time in hours. The following data obtained: Amount of GAS (liters) Running Time (hours) 0.6 2.1 2.4 10 15 20 The researcher fit the linear model -Xß + є, where β-(A, β)'. 1. What are the required assumptions to fit the linear model? 2. Find the estimated parameters using the Maximum Likelihood method 3. Compute the first fitted value (i) and its corresponding residual. 4. Show that for any linear model, where RSS is the residual sum of squares and TSS is the total sum of squares. 5. What is the smallest possible variance of a linear estimator of A? (you could write it in term of ơ2) 6. What is the average running time a car would take to consume 17 liters of GAS based on your estimated model? 7. Find a 95% confidence interval for the regression coefficient? (You could use RSS-62.86 and the tabulated 8. Explain what is the difference between a confidence interval and a prediction interval for a given set of ue T3,o.025 3.18) predictor variables? 9. Find the confidence level for the simultaneous 95% confidence region for all the parameters jointly? Question4 (30 points) A research to study the amount of the GAS fuel a 4x 4 car uses, given the running time in hours. The following data obtained: Amount of GAS (liters) Running Time (hours) 0.6 2.1 2.4 10 15 20 The researcher fit the linear model -Xß + є, where β-(A, β)'. 1. What are the required assumptions to fit the linear model? 2. Find the estimated parameters using the Maximum Likelihood method 3. Compute the first fitted value (i) and its corresponding residual. 4. Show that for any linear model, where RSS is the residual sum of squares and TSS is the total sum of squares. 5. What is the smallest possible variance of a linear estimator of A? (you could write it in term of ơ2) 6. What is the average running time a car would take to consume 17 liters of GAS based on your estimated model? 7. Find a 95% confidence interval for the regression coefficient? (You could use RSS-62.86 and the tabulated 8. Explain what is the difference between a confidence interval and a prediction interval for a given set of ue T3,o.025 3.18) predictor variables? 9. Find the confidence level for the simultaneous 95% confidence region for all the parameters jointly?