Answer Happy

A response variable of interest y was studied as a function of several predictors Answer the following questions using the Minitab results in this file. For all statistical conclusions use a significance level of 0.01 unless specified otherwise. 1. What are the values of k and p in this moder? 2. How many samples were used to build this moder? 3. What is the proportion of the variability of the data explained by the model? Does this supoest a good predictive moder? 4. Is the regression significant? Why? 5. State the hypotheses for the partial F test of in this Minitab output. Practice for any other variable

- WORKSHEET 1 Matrix Plot of Y, X1, X2, X3, X4 Matrix Plot of Y, X1, X2, X3, X4 2000 XI

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