**1.**When the null hypothesis, H_{0}: b_{1 }= b_{2 }= b_{3}=_{ }0, is rejected, the interpretation should be:There is no linear relationship between y and any of the three independent variables There is a regression relationship between y and at least one of the three independent variables All three independent variables have a slope of zero All three independent variables have equal slopes There is a regression relationship between y and all three independent variables

**2.**Suppose that in a multiple regression the F is significant, but none of the t-ratios are significant. This means that:Multicollinearity may be present Autocorrelation may be present The regression is good A nonlinear model would be a better fit None of the above

**3.**What is the difference between R^{2}and the adjusted R^{2}?The adjusted R ^{2}always increases as more independent variables are added to the modelThe adjusted R ^{2}is smaller in this case because the constant term is negativeThe adjusted R ^{2}adjusts explanatory power by the degrees of freedomThe adjusted R ^{2}is always smaller than R^{2}The adjusted R ^{2}adjusts explanatory power by division by the standard error of each coefficient

The data are shown below:

The Minitab regression analysis follows:

Analysis of Variance**4.**Write the regression equation, letting undergraduate GPA be variable 1 and standard scores be variable 2.Y = 0.4775 x _{1}+ 0.0013392x_{2}Y = 0.2059 + 0.1630x _{1 }+ 0.0006693x_{2}None of the others is correct Y = 1.1066 + 0.4775x _{1}+ 0.0013392x_{2}Not enough information given

**5.**At the 5% level of significance, are undergraduate scores and standard scores significant?Both are significant Neither are significant Only undergraduate GPA is significant Only standard scores are significant Not enough information to determine

**6.**Compute R^{2}.99.4% 98.6% 20.8% Very close to 100% Insufficient information to determine

**7.**All of the following are possible effects of multicollinearity EXCEPT:The variances of regression coefficients estimators may be larger than expected The signs of the regression coefficients may be opposite of what is expected A significant F ratio may result even though the t ratios are not significant Removal of one data point may cause large changes in the coefficient estimates The VIF is zero

**8.**Correlation of the values of variables with values of the same variables lagged one or more time periods back is called:Multicollinearity A transformation Autocorrelation Variance inflation Interaction

**9.**Dummy variables are used when:Qualitative variables are involved in the model Quantitative variables are involved in the model Doing residual analysis Making transformations of quantitative variables None of the above

**10.**A multiple regression model with two independent variables exhibits a highly significant F-ratio, but each variable's individual t-statistic is insignificant. The most likely cause of such a situation is ____________Heteroskedasticity Homoskedasticity Multicollinearity Non-independence of residuals Non-normality of residuals

**11.**In a regression analysis involving a lagged predictor variable, the two-tailed critical lower and upper values for the Durbin-Watson test statistic are, respectively, 1.50 and 1.70. The observed Durbin-Watson test statistic is 1.32. Based on this evidence we would infer _______________.Negative autocorrelation Itive autocorrelation Thing; the test is inconclusive Eteroscedasticity Lticollinearity

**12.**In a multiple regression study with 60 observations, an analyst is considering whether or not to include a fourth predictor variable. The SSE of the model when the fourth variable is included is 28,422. The SSE of the model when the fourth variable is not included is 30,224. Based on the partial F-statistic of ___________ we would conclude that the additional variable ____________ the model.4.71; does not significantly improve 5.35; significantly improves 1.74; does not significantly improve 2.38; does not significantly improve None of the above

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