Answer Happy

14. What are the confidence intervals for the mean response of a regression model versus the mean response prediction of the interval? 15. Are there problems with multicollinearity in this model? Why? 16. Will you recommend the presented model taking into consideration the information provided? Why?

WORKSHEET 1 Regression Analysis: Y versus X1, X2, X3, X4 Method Cross-validation 10-fold Regression Equation v. 12.27 +0.00739 X1 +0.000584 X2 -0.330 X3 -0.00946 XA Coefficients Term Coef SE Coef 95% CI Constant 12.27 2.02 (8.20. 16.33) X1 0.00739 0.00693 -0.00655, 0.02133) X2 0.000584 0.000722 (-0.000868, 0.002035) X3 -0.330 0.235 (-0.802, 0.141) X4 -0.00946 0.00489 (-0.01929, 0.00036) T-Value P.Value VIF 6.07 0.000 1.07 0.292 1.40 0.423 1.17 -1.41 0.166 1.29 -1.94 0.059 1.08 0.81 Model Summary SR-sq Risqlad PRESS R-sqlpred) AICC BIC 10-fold 5 10-fold R-sq 1.60126 14.37% 7.23% 146.777 0.00% 208.89 218.88 1.67384 0.00% Analysis of Variance Source DF Seq SS Contribution Adj SS Adj MS F.Value P-value Regression 4 20.654 14,37% 20.654 5.164 2.01 0.107 X1 1 1.926 1.34% 2.914 2.914 1.14 0.292 X2 1 0.918 0.64% 1.676 1.676 0.65 0.423 X3 1 8.195 5.70 5.083 5.083 1.98 0.166 X4 1 9.614 6.69 9.614 9.614 3.75 0.059 Error 48 123.074 85.63% 123.074 2.564 Total 52 143.728 100.00% Fits and Diagnostics for Unusual Observations Obs Fit SE Fit 95% CI Resid Std Resid Del Resid HI Cook's D 4 8.900 10.165 0.948 (8.258, 12072) -1.265 -0.98 -0.98 0.350694 0.10 11 8.500 7.406 0.932 (5.533.9.279) 1.094 0.84 0.84 0.338450 0.07 315.000 8.969 0.299 (8.368, 9.571) -3.969 -2.52 -2.68 0.034895 0.05 43 3.600 9.240 0.371 18.494, 9.986) -5.640 -3.62 -4.20 0.053688 0.15 Obs DFITS 4 -0.72017 X 11 0.59878 х 31 0.50981 R 43 -1.00106 R

R Large residual x Unusual Residual Plots for Y Normal Probability Plot Versus Fits 99 Percent So Residual 2 10 Residual Histogram Fitted Value Versus Order Frequency Residual ខ្ញុំ ។ 15 20 25 30 35 40 45 50 Observation Order Residual

WORKSHEET 1 Probability Plot of RESI Probability Plot of RESI Normal 99 Mean SiDev N AD p-Value 127361E-15 1.535 53 0.845 0.028 95 90 80 Percent 70 60 50 30 20 10 5 4 2 2 RESI

| WORKSHEET 1 Test for Equal Variances: RESI versus Groups Method Null hypothesis All variances are equal Alternative hypothesis At least one variance is different Significance level q+0.05 Bartlett's method is used. This method is accurate for normal data only. 95% Bonferroni Confidence intervals for Standard Deviations Groups N StDev ai 1 9 1.38249 (0.82550, 3.46171) 2 9 1.05535 (0.63016, 2.64256) 3 9 1.25187 (0.74751, 3.13464) 4 9 1.70069 (1.01551, 4.25848) 5.9 1.98708 (1.18651, 4.97558) 6 8 1.65179 (0.95951, 4.52358) Individual confidence level 99.1667% Tests Test Method Statistic P-value Bartlett 3.87 0.569

WORKSHEET 1 Test for Equal Variances: RESI versus Groups Method Null hypothesis All variances are equal Alternative hypothesis At least one variance is different Significance level q=0.05 95% Bonferroni Confidence intervals for Standard Deviations Groups N Stev CI 1 9 1.38249 (0.733377, 3.6869) 2 9 1.05535 (0.549615, 2.8668) 3 9 1.25187 (0.673133, 3.2937) 4 9 1.70069 (0.361950, 11.3050) 5 9 1.98708 (0.540562, 10.3336) 6 8 1,65179 (0.504700, 8.0660) Individual confidence level = 99.56674 Tests Method Multiple comparisons Levene Test Statistic P.Value 0.880 0.19 0.963

WORKSHEET 1 Runs Test: RESI Descriptive Statistics Number of Observations N KSK >K 53 -0.0000000 23 30 * = sample mean Test Null hypothesis H: The order of the data is random Alternative hypothesis H. The order of the data is not random Number of Runs Observed Expected p-value 25 27.04 0.565