Answer Happy

A small data set on n=4 cases for examining the regression relation between a response variable Y and two predictor variables X1 and X2 is shown in the following table. > df X1 X2 Y 1 14 25 301 2 19 32 327 3 12 22 246 4 11 15 187 > The linear model output is given by # > summary (mod) # # Call: # im (formula = Y ~ X1 + X2, data = df) # # Residuals: # 1 2 3 4 # 18.7621 -5.2919 -13.9513 0.4811 # # coefficients: # Estimate Std. Error t value Pr(>[t # (Intercept) 80.930 57.944 1.397 0.396 # x1 -5.845 11.745 -0.498 0.706 # x2 11.325 5.931 1.909 0.307 # # Residual standard error: 23.98 on 1 degrees of freedom # Multiple R-squared: 0.9504, Adjusted R-squared: 0.8511 # F-statistic: 9.576 on 2 and 1 DF, p-value: 0.2228

(a) Using the output write down the regression equation. (b) Fill up the ANOVA Table: F-Ratio P-Value Source of Variation Degrees of Freedom Sum of Squares Mean Square Regression Error Total 6 The Hat Matrix for this problem is given by #> round(H,4) #[,1] [,2] [,3] [,4] #[1,] 0.3877 0.1727 0.4553 -0.0157 # [2] 0.1727 0.9513 -0.1284 0.0044 # [3,] 0.4553 -0.1284 0.6614 0.0117 # [4,] -0.0157 0.0044 0.0117 0.9996 #>

(c) What could you conclude about the observations? Any potential Outliers? (d) What's the internally studentized residual ( rı) for the first observation? (e) What is the externally studentized residual (ta) for the first observation? (f) What's the Cook's distance (D1) for the first observation? (g) What is the variance of the residual for the first observation?