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Analysis of Regression Models and Hypothesis Testing in Predicting Dependent Variables

Explores regression models and hypothesis testing for predictive analysis.

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    1 Analysis of Regression Models and Hypothesis Testing in Predicting Dependent Variables 578 Assignment - 5 (Chs. 13 and 14 ) - solutions: Due by m idnight of Sunday, December 2 nd , 2012: drop box 4): 7 0 points True/False (One point each) Chapter 13 1. The standard error of the estimate (standard error) is the estimated standard deviation of the distribution of the independent variable (X). FALSE it is the estimate of the standard deviation of the error term 2. In a simple linear regression model, the coefficient of determination only indicates the strength of the relationship between independent and dependent variable, but does not show whether the relationship is positive or negative. TRUE R 2 is greater than or equal to 0, no negative 3. When using simple regression analysis, if there is a strong correlation between the independent and dependent variable, then we can conclude that an increase in the value of the independent variable causes an increase in the value of the dependent variable. FALSE the stron g correlation could be negative 4. The error term is the difference between an individual value of the dependent variable and the corresponding mean value of the dependent variable. FALSE it is the difference between an individual value of the dependent variable and the corresponding predicted value (not the mean value) : residual and error term are the same thing 5. In bi - variate regression the Coefficient of Determination is always equal to the square of the correlation coefficient. TRUE

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    2 6. In Regression Analysis if the variance of the error term is constant, we call it the Heteroscedasticity property. FALSE ( instruction page 10 - 11) Chapter 14 7 . When the F test is used to test the overall significance of a multiple regression model, if the null hypothesis is rejected, it can be concluded that all of the independent variables X 1 , X 2 ,  X k are significantly related to the dependent variable Y. FALSE we can conclude that at least one (not all) …. 8 . An application of the multiple regression model generated the following results involving the F test of the overall regression model: p - value =.0012, R 2 =.67 and s=.076. Thus, the null hypothesis, which states that none of the independent variables are significantly related to the dependent variable, should be rejected even at the .01 level of significance. TRUE since p - value is less than 0.01 9 . High Multicollinearity problem occurs when the Independent variables are high l y correlated with the Dependent variable. FALSE It occurs when there is high linear relation among the Independent variables. 10 . The assumption of independent error terms in regression analysis is often violated when using time series data and is called the problem of Autocorrelation . TRUE see Instructions 11 . Homoscedasticity problem occurs when the assumption of con s tant error variance is violated. FALSE . This problem is called Heteroscedasticity and frequently occurs in cross - sectional data . Multiple Choices (Two points each) Chapter 13

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    3 1. All of the following are assumptions of the error terms in the simple linear regression model except : A. Errors are normally distributed B. Error terms have a mean of zero C. Error terms have a constant variance D. Error terms depend on the explanatory variable (Instruction page 10 - 11, Book page 530) 2 . The point estimate of the variance in a regression model is A. SSE B . MSE C. s e D. b 1 3 . The least squares regression line minimizes the sum of the A. Sum of Differences between actual and predicted Y values B. Sum of Squared differences between actual and predicted X values C. Sum of Absolute deviations between actual and predicted X values D. Sum of Absolute deviations between actual and predicted Y values E . Sum of Squared differences between actual and predicted Y values 4 . The ___________ the R 2 and the __________ the s (standard error), the stronger the relationship between the dependent variable and the independent variable. A. Higher, lower B. Lower, higher C. Lower, lower D. Higher, higher 5 . In simple bivariate regression analysis, if the correlation coefficient is a positive value, then A. The Y intercept must also be a positive value . B. The coefficient of determination can be either positive or negative, depending on the value of the slope . C. The least squar es regression equation could either have a positive or a negative

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