A group of 63 radiometers have two calibration runs and a final run. How well do the two calibration runs predict performance on the final run? The following are some quantities of interest: (X'X)^-1 =( 0.9129168 -0.009815022 -0.000711238 = (-0.009815022 0.0001497241 -0.00004158056 -0.000711238 -0.00004158056 0.0000581235 ) X'y =( 4871.0 426011.0 367576.5)
y'y =Σ^ 63_i=1 y_1^2 = 411222.7041 Σ^63_i=1 y_i = 674.7227 (a) Calculate the least squares estimates of the slopes for hourly 1 and hourly 2 and the intercept. (b) Use the equation of the fitted line to predict the final run score for a radiometers who scored 70 on calibration run 1 and 85 on calibration run 2. (c) If a radiometer that scores 80 on calibration run 1 and 90 on calibration run 2 gets an 85 on the final run, what is its residual? (d) What is the value of ô^2? (e) Test the significance of regression for this regression model. Use alpha= 0,05