True/False(One point each)
Chapter
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 R2 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.
FALSEthe 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 X1, X2, ?Xk 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, R2=.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 highly 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 constant error variance is violated. FALSE. This problem is called Heteroscedasticity and frequently occurs in cross-sectional data.
Multiple Choices(Two points each)
Chapter 13
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. se
D. b1
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 R2 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 squares regression equation could either have a positive or a negative slope.
D. The standard error of estimate can either have a positive or a negative value.
E. The slope of the regression line must also be positive.
(the slope coefficient and correlation coefficient have the same sign in bivariate regression- also obvious from the interpretation of the slope in Instruction- but note that the relation could be weak or strong. Positive sign only shows the direction not the magnitude.)
6. A researcher wants to explore the relationship between the grades students receive on their Midterm test and their Final test score. The following data present the Midterm and Final scores for ten students. What is the correlation coefficient?
Mid Fin
180 280
195 280
210 300
225 316
240 320
255 350
255 370
264 320
265 400
290 350
A. 0.556
B. 0.645
C. 0.738
D. 0.802
E. 0.905
The MegaStat result is given below:
Correlation Matrix
Mid Fin
Mid 1.000
Fin .802 1.000
10 sample size
Chapter 14
7. Which is not an assumption of a multiple regression model?
A. Positive autocorrelation of error terms
B. Normality of error terms
C. Independence of error terms
D. Constant variation of error terms
E. Independence of error terms with X variables
see Instructions
8. A multiple regression analysis with 22 observations on each of four independent variables and the dependent variable would yield ______ and _______ degrees of freedom respectively for regression (explained) and error.
A. 3, 17
B. 4, 20
C. 4, 18
D. 3, 20
E. 4, 17
df for regression = k = 4 and df for error = n-k-1 = 22-4-1 = 17
9. Consider the following partial computer output for a multiple regression model.
What is R2?
A. 31.308%
B. 76.95%
C. 77.72%
D. 72.63%
E. 23.1%
where the denominator is SST
10. Consider the following partial computer output for a multiple regression model.
What is adjusted R2?
A. 31.308%
B. 76.95%
C. 87.72%
D. 72.63%
E. 23.1%
R ¯2 = 1- [SSE/(n-k-1)]/[SST/(n-1)] = 1- (9.378/16)/(40.686/19) =.7263
11. In multiple regression analysis, the mean square regression divided by mean square error yields the:
A. Standard error
B. F statistic
C. R2
D. Adjusted R2 or
E. T statistic
see Instructions
12. A particular multiple regression model has 3 independent variables, the sum of the squared error is 7680 and the total number of observations is 34. What is the value of the standard error of estimate?
A. 256
B. 232.72
C. 225.89
D. 16
E. 15.03
The df for error = 34- 3-1 = 30 and the standard error of estimate is √MSE = √(7680/30) = 16.
Essay Type (Five points each)
Chapter 13
1. Use the following results obtained from a simple linear regression analysis with 12 observations.
Y ^ = 37.2895 - (1.2024)X
r2 = 0.6744 sb1 = 0.2934
Test to determine if there is a significant negative relationship between the independent and dependent variable at =.05 and .01
Reject H0, There is a significant negative relationship between dependent and independent variable. H0: b1≥0 and Ha: b1<0 on