Suppose that data has been collected for 200 multierigine aircraft For this example, the explanatory variable of interest is the maximum takeoff weight of the aircraft in thousands of kilograms (labelled weight), The response variable is the price of the aircraft in millions of US dollars (labelled price) A simple linear regression analysis is carried out with the response variable and the explanatory variable. The results 01 the least squares analysis are displayed below: Call: 1m(formula = price ~ weight) Residuals: Min 10 Median 30 Max 46-050 -15-364 1.373 15.156 51.607 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 1.47646 4.02156 0.367 0.714 weight 0.55815 0.01223 70.191
t 0.05 c No, because we have p 0 05 f. Using the fact that t198, 0.975 = 1.972, construct a 95% confidence interval for 1. The lower bound of the 95% confidence interval is and the upper bound of the 95% confidence interval is .(4 marks) g. The estimated regression model can be written down as: (2 marks) o Price = 0.858 + -1.476 x weight Weight = 0.858 + -1.476 x price Weight = -1.476 + 0.858 x price Price = -1.476 + 0.858 x weight h. Use the regression model equation to predict the price (in millions of dollars) of an aircraft that weighs 350 thousand kilograms: (2 marks) Now suppose we are interested in estimating aircraft prices associated with an aircraft weight of 450 thousand kilograms. In a random order, the confidence and prediction intervals are provided as follows: fit lwr upr 1 384. 689 380. 269 389. 110 1 384. 689 344. 947 424. 432 Use this information to answer the following: i. The lower bound of the confidence interval is and the upper bound of the confidence interval is (4 marks) j. The lower bound of the prediction interval is and the upper bound of the prediction interval is (2 marks) k. Which of the below choices provide the best justification as to why the confidence and prediction intervals are different? (3 marks) o The prediction interval is an interval for the estimate for the average aircraft weight whereas the confidence interval is an estimate for the weight of a single aircraft. The confience interval is wider to take into account the error variance. o The confidence interval is an interval for the estimate for the average aircraft price whereas the prediction interval is an estimate for the price of a single aircraft. The prediction interval is wider to take into account the error variance. o The prediction interval is an interval for the estimate for the average aircraft price whereas the confidence interval is an estimate for the price of a single aircraft. The confience interval is wider to take into account the error variance. The confidence interval is an interval for the estimate for the average aircraft weight whereas the prediction interval is an estimate for the weight of a single aircraft. The prediction interval is wider to take into account the error variance
