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6. State the test statistic value for the partial F-test of What is the conclusion and meaning of this test? Practice for any other variable 7. What is the estimate of o? 8. State the hypotheses for the significance t-test of B., Practice for any other coefficient. 9. Construct the (1-a)% confidence interval (CI) for 8, Establish the critical value used to construct this interval. Practicn for any other variable 10. Use the previous Ci to provide a statistical conclusion. What is the meaning of such a conclusion? 11. List the three assumptions that must be satisfied with their subjective & objective tools and verify if those are satisfied with the model constructed here. • Assumption 1: Plot axis names: Test: Satisfied? • Assumption 2: Plot axis names: Test: Satisfied? • Assumption 3: Plot axis names: Test satisfied? How many possible influential observations does Minitab identity State which criteria was used for each observation. Evaluate if these possible observations identified by Minitab will be possible influential observations using all the criteria discussed in class. State why and present identify the residuals or metrics used. What can you do if an actionable causes associated with influential observations at you were implementing the variable selection methods, which predictor will be the first candidate to be removed from the model for each method? Use an (enter -0.1, 0.1) What are the confidence intervals for the mean response of a regression model versus the mean response prediction of the interval? Are there problems with multicollinearity in this model? Why? 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 Y 12.27 -0.00739X1 +0.000584 X2 -0.330 X3 -0.00946 X4 Coefficients Term Coef SE Coet 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 0.166 1.29 -1.94 0.059 1.08 0.81 Model Summary SR-sq Risqladi) PRESS R-sq[pred) AICC BIC 10-fold 10-fold Rusq 1.60126 14.37% 7.23% 146.777 0.00% 208.89 218.88 1.67384 0.004 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 + 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, 12.072) -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