1. A set of regression results for this problem are available in this Module • Y
ID: 3051361 • Letter: 1
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1. A set of regression results for this problem are available in this Module • Your job is to provide a statistical and economic interpretation of the results focusing on: a. Tests for significance of the parameters (t-tests). You testing to see if the parameters are statistically different from zero. If they are not they are not significant or there is no relationship between the variables. pp. 185-187 b. Amount of variation explained by the equation (adjusted R-squared), pp. 194-195 c. Analysis of Variances (F-test) for significance of entire equation. The equation is not significant if the F-test fails. Failure indicates that all of the parameters are simultaneously zero; the equation is not valid. If at least one of the independent variables is non-zero the equation will be significant. pp. 195-196 d. Evidence of multi-collinearity (inconsistent F and t tests or incorrect economic signs with a significant t tests). Multi-collinearity exists when the F test says the equation is significant, yet each of the t tests are not significant. The problem is that collinearity between “independent” variables prevents the regression program from determining the effects of the individual variables. This problem can also cause the signs associated with known economic relationships to be incorrect. p.197 e. Autocorrelation (Durbin-Watson statistic), p. 199 REGRESSION MISSING LISTHISE /STATISTICS COEFF OUTS BCOV R ANOVA COLLIN TOL /CRITERIA-PIN.05) POUT.10) /NOORIGIN /DEPENDENT YQD METHOD-ENTER X1Price X2Income /RESIDUALS DURBIN Regression Variables Entered/Removed Variables Removed Method Entered X2-Income X1-Price Enter a. Dependent Variable: Y=QD b. All requested variables entered Model Summary Adjusted R Square Std. Error of the R Square Estimate Durbin-Watson 984 968 964 7.205 2.314 a. Predictors: (Constant), X2-Income, X1 Price b. Dependent Variable: Y QD ANOVA Sum of df Mean Square Sig 26884 298 882.502 27766.800 13442.149 258.942 Residual 17 19 51.912 Total a. Dependent Variable: Y QD b. Predictors: (Constant), X2-Income, X1-PriceExplanation / Answer
a. t 0.025;17 = 2.11
For all the variables i.e constant, x1 and x2, | t statistic | > 2.11 which implies that all the variables are statistically significant.
b. Adjusted R square = 0.964 implies 96.4% of the total variation is explained by the regression model fitted to the data.
c. From the F table, F 0.05;2,17 = 3.5915 < Calculated F = 258.942 which implies that the regression is significant enough to be fitted to the data.
d. Correlations among the predictors are large and VIF > 4 implies that it needs further investigation to detect multicollinearity.
e. Durbin Watson statistic = 2.314 > 2 implies there is a presence of negative correlation among the successive error terms.
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