Content Bb 20954665 Bb 20954673 X C learn-us-east-1-prod-fleet02-xythos.content.blackboardcdn.com/5cc71db6522fe/20954673?X-Blackboard-Expiration=1634860800000&X-Blackboard-Signature=JHv... * To 20954673 1 / 3 100% + Setup: Consider data on per-capita beer consumption (y), per-capital real income (x1), and the relative price of beer (X2). The linear regression model Yi = Bo + Bili + B2i2 + E; is estimated from n = 21 observations. Using a regression program, we find that the estimates and their standard errors (given in parentheses) are Bo = 1.40(0.50) B1 = 1.10(0.15) B2 = -0.90(0.30) 1 A partially completed ANOVA table is as follows: Source SS df MS F Regression Error 81 Total 189 Questions: 1. Calculate a 95% confidence interval for B2. Round your final answer to 3 decimals. 2 2. Complete the above ANOVA table. 3. Test the null hypothesis that both regression coefficients are zero (i.e. the overall model is significant in explaining the response). Use a significance level of a = 0.05. Be sure to include: . Hypotheses . Decision (Reject or not) . Test Statistic Value . Conclusion . Critical Region or P-Value 3 4. Conduct a partial t-test for S, at the a = 0.05 significance level to determine S, has a significant impact on the response. Interpret your results. Be sure to include: . Hypotheses . Decision (Reject or not) . Test Statistic Value . Conclusion . Critical Region or P-Value 5. Calculate the multiple coefficient of determination, R2 and the Adjusted R2 value.Content Bb 20954665 Bb 20954673 X C learn-us-east-1-prod-fleet02-xythos.content.blackboardcdn.com/5cc71db6522fe/20954673?X-Blackboard-Expiration=1634860800000&X-Blackboard-Signature=JHv... * To 20954673 2 / 3 100% + Setup: We have information on 3 variables (x1-x3) from 18 subjects. We run various models. Results are shown below. Full Model: y = 63.14 + 1.88x1 + 0.30x2 - 0.43x3 Analysis of Variance Sum of Source DF Squares Square F Value Pr > F Model 3 6292.41660 2097.47220 4.82 0.0166 Parameter Estimates Error 14 6097.19451 435.51389 Variance Corrected Total 17 12390 Variable DF Parameter Standard Estimate Error t Value Pr > It| Inflation Intercept 1 63.14387 18.33827 3.44 0.0040 Root MSE 20.86897 R-Square 0.5079 x1 1.87598 0.57089 3.29 0.0054 1.31184 Dependent Mean 81.27778 Adj R-Sq 0.4024 *2 1 0.30019 0.48792 0.62 0.5483 1.72503 Coeff Var 25.67611 -0.43218 0.50676 -0.85 0.4081 1.62162 Model without x3: y = 56.25 + 1.79x1 + 0.09x2 Model without X2: y = 68.27 + 1.98x1 - 0.2723 Analysis of Variance Analysis of Variance Sum o Mean Sum of Mean 2 Source DF Squares Square F Value Pr > F Source DF Squares Square F Value Pr > F Model 2 5975.66853 2987.83427 6.99 0.0072 Model 2 6127.56211 3063.78106 7.34 0.0060 Error 15 6413.94258 427.59617 Error 15 6262.04900 417.46993 Corrected Total 17 12390 Corrected Total 17 12390 Model without x1: y = 53.82 + 0.78x2 - 0.14x3 Analysis of Variance Sum of Mean 3 source DF Squares e F Value Pr > F Model 2 1589.72777 794.86389 1.10 0.3570 Error 15 10800 719.99222 Corrected Total 17 12390 Model Estimating x1: $1 = -4.97 + 0.26x2 + 0.16x3 Analysis of Variance Sum of Mean Source DF Squares Square F Value Pr > F Model 2 416.70524 208.35262 2.34 0.1306 Root MSE 9.43843 R-Square 0.2377 Dependent Mean 11.94444 Adj R-Sq 0.1361Content Bb 20954665 Bb 20954673 X C learn-us-east-1-prod-fleet02-xythos.content.blackboardcdn.com/5cc71db6522fe/20954673?X-Blackboard-Expiration=1634860800000&X-Blackboard-Signature=JHv... To # 20954673 3 / 3 100% + Model Estimating $1: $1 = -4.97 + 0.26x2 + 0.16x3 Analysis of Variance Sum of Mean Source DF Squares Square F Value Pr > F Model 2 416.70524 208.35262 2.34 0.1306 Root MSE 9.43843 R-Square 0.2377 Error 15 1336.25920 89.08395 Dependent Mean 11.94444 Adj R-Sq 0.1361 Corrected Total 17 1752.96444 Coeff Var 79.01941 2 2 Model Estimating X2: 32 = 17.07 + 0.35x1 + 0.53x3 Analysis of Variance Sum of Mean Source DF Squares Square F Value Pr > F 3 Model 2 1326.37067 663.18534 5.44 0.0168 Root MSE 11.04357 R-Square 0.4203 Error 15 1829.40711 121.96047 Dependent Mean 42.11111 Adj R-Sq 0.3430 Corrected Total 17 3155.77778 Coeff Var 26.22484 Model Estimating X3: $3 = 15.95 + 0.20x1 + 0.49x2 Analysis of Variance Sum of Source DF Squares Square F Value Pr > F Model 2 1054.17761 527.08880 4.66 0.0266 Root MSE 10.63286 R-Square 0.3833 Error 15 1695.86517 113.05768 Dependent Mean 39.13889 Adj R-Sq 0.3011 Corrected Total 17 2750.04278 Coeff Va 27.16699Content Bb 20954665 Bb 20954673 X C learn-us-east-1-prod-fleet02-xythos.content.blackboardcdn.com/5cc71db6522fe/20954673?X-Blackboard-Expiration=1634860800000&X-Blackboard-Signature=JHv... * To 20954673 3 / 3 100% + Model Estimating X2: $2 = 17.07 + 0.35x1 + 0.53x3 Analysis of Variance Sum of Mean Source DF Square Square F Value Pr > F Model 2 1326.37067 663.18534 5.44 0.0168 Root MSE 11.04357 R-Square 0.4203 Error 15 1829.40711 121.96047 Dependent Mean 42.11111 Adj R-Sq 0.3430 Corrected Total 17 3155.77778 Coeff Var 26.22484 Model Estimating X3: $3 = 15.95 + 0.20x1 + 0.49x2 Analysis of Variance Sum of Mean Source DF Squares Square F Value |Pr Model 2 1054.17761 527.08880 4.66 0.0266 Root MSE 10.63286 R-Square 0.3833 2 Error 15 1695.86517 113.05768 Dependent Mean 39.13889 Adj R-Sq 0.3011 27.16699 Corrected Total 17 2750.04278 Coeff Var Questions: 6. Using the VIF, is multicollinearity present and why? Then, provide the calculations that give the VIF value for x1. 7. Calculate the partial R2 value R21,3- 3