**Statistics 578 Homework**

**578Assignment-5 (Chs. 13 and 14)-solutions: Due by midnight of Sunday, December 2 ^{nd}, 2012: drop box 4): 70 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.

**R**

__TRUE__^{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 strong 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__

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}, ¼X_{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*=.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.

^{2}**since p-value is less than 0.01**

__TRUE__9. High Multicollinearity problem occurs when the Independent variables are highly correlated with the Dependent variable.

**It occurs when there is high linear relation**

__FALSE__**among the Independent variables.**

**Category:**Business, General Business

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