Analysis of Regression Models and Hypothesis Testing in Predicting Dependent Variables

Name: Analysis of Regression Models and Hypothesis Testing in Predicting Dependent Variables
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Explores regression models and hypothesis testing for predictive analysis.

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Analysis of Regression Models and Hypothesis Testing in Predicting
Dependent Variables
578Assignment-5 (Chs. 13 and 14)-solutions: Due by midnight of Sunday,
December 2nd, 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.
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

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 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

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. 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

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Statistics

Analysis of Regression Models and Hypothesis Testing in Predicting Dependent Variables

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