Part one: True/False Statements:
1. Multiple linear regression can handle both continuous and categorical independent variables.
2. Multicollinearity between independent variables can lead to unreliable and unstable estimates
of the regression coefficients.
3. The p-value associated with a coefficient in multiple linear regression indicates the strength
of the relationship between the independent variable and the dependent variable.
4. Outliers can have a significant impact on the coefficients and predictions in multiple linear
regression.
5. In multiple linear regression, the slope coefficient represents the change in the dependent
variable associated with a one-unit change in the corresponding independent variable,
holding all other variables constant.
6. Assumptions of linearity, normality, and constant variance (homoscedasticity) need to be met
for accurate inference and valid predictions in multiple linear regression.
7. Multicollinearity occurs when there is a strong linear relationship between two or more
independent variables, making it difficult to determine the individual effects of each variable
on the dependent variable.
8. The residual plot should ideally show a random scatter pattern around a horizontal line to
satisfy the assumption of homoscedasticity in multiple linear regression.
9. If the residuals in a linear regression model follow a normal distribution, the assumption of
normality is satisfied.
10. Violations of the assumption of independence in linear regression can lead to biased
coefficient estimates.
11. Heteroscedasticity refers to the situation where the variability of the residuals is not constant
across all levels of the independent variables.
12. If the dependent variable and the residuals in a linear regression model exhibit a curved
pattern in a residual plot, it suggests the violation of the linearity assumption.
13. Violations of the assumptions of the classical linear regression model will always lead to
entirely invalid results.
14. Autocorrelation refers to the correlation between the current observation and the previous
observation(s) in a time series.
15. When using regression analysis with time series data, it is not necessary to account for the
correlation among the error terms.
16. Panel data regression models can account for time-invariant variables.
Part Two: Multiple-Choice Questions:
1. What is the purpose of multiple linear regression?
A. To predict the value of a dependent variable based on one independent variable
B. To predict the value of a dependent variable based on multiple independent variables
C. To analyze categorical data
D. To perform classification tasks
2. Which of the following is an assumption of multiple linear regression?
A. Normal distribution of the dependent variable
B. No multicollinearity among the independent variables
C. Homoscedasticity of the residuals
D. All of the above
3. How is R-squared interpreted in multiple linear regression?
A. It represents the percentage of variance in the dependent variable explained by the
independent variables.
B. It represents the percentage of variance in the independent variables explained by the
dependent variable.
C. It measures the correlation between the dependent and independent variables.
D. It represents the mean of the dependent variable.
4. What is the purpose of the adjusted R-squared in multiple linear regression?
A. To measure the amount of variance explained by the independent variables
B. To penalize model complexity and account for the number of predictors
C. To determine the statistical significance of the regression coefficients
D. To assess the linearity assumption of the model
5. What is the purpose of residual analysis in multiple linear regression?
A. To check for violations of regression assumptions
B. To assess the accuracy of predictions
C. To identify influential data points
D. All of the above
6. Which assumption of the classical linear regression model is violated if the relationship
between the dependent and independent variables is nonlinear?
A. Linearity
C. Homoscedasticity
B. Normality
D. Independence
7. If the residuals in a linear regression model exhibit a funnel-shaped pattern in a residual
plot, which assumption is likely violated?
A. Linearity
C. Homoscedasticity
B. Normality
D. Independence
8. Which assumption of the classical linear regression model is violated if the residuals
exhibit a systematic pattern over time?
A. Linearity
C. Homoscedasticity
B. Normality
D. Independence
9. If the residuals in a linear regression model are not normally distributed, which assumption
is violated?
A. Linearity
C. Homoscedasticity
B. Normality
D. Independence
10. Violations of the assumption of independence in linear regression can lead to:
A. Underestimation of standard errors
B. Overestimation of standard errors
C. Biased coefficient estimates
D. Inflated R-squared values
11. Heteroscedasticity in linear regression refers to:
A. Nonlinear relationship between variables
B. Nonconstant variance of residuals
C. Lack of independence among residuals
D. Violation of the normality assumption
12. What is a time series variable?
A. A variable that changes over time
B. A variable that remains constant over time
C. A variable with a fixed value across all observations
D. A variable that is unrelated to time
13. In time series regression, what is the dependent variable?
A. Time
C. Independent variable
B. Predictor variable
D. Response variable
14. What is the first step in analyzing time series data?
A. Plotting the data
C. Removing outliers
B. Transforming the data
D. Fitting regression models
15. What is panel data?
A. Data collected over a short period of time
B. Data collected from multiple sources
C. Data collected from multiple cross-sectional units over time
D. Data collected from a single source
16. What is the advantage of panel data regression models over cross-sectional or time series
regressions?
A. They allow for better prediction accuracy
B. They capture individual-level and time-specific effects
C. They have fewer assumptions
D. They are less computationally intensive
17. Consider simple regression model with coefficient standard errors calculated using the
common formula. Which of the following statement is correct regarding the standard error
estimator for slope coefficient?
A. It varies positively with the spread of X about its mean value
B. It varies positively with the spread of X about zero
C. It varies positively with the sample size T
D. It varies positively with the square root of the residual variance
E. None
18. E(ut) = 0 says that
A. Dividing the error by explanatory variable results in a zero
B. The sample mean Ys is much larger than zero
C. The condition the distribution of the error term has a zero mean
D. The sample mean Xs is equal to zero
19. Which of the following could be used as test for autocorrelation?
A. White’s test
D. The Crack tests
B. The Durbin Watson (DW) test
E. All
C. The RESET tests
20. In y = β1 + β2X1 +ύi, the ύi gives the difference between
A. The actual and estimated X values
B. The actual and estimated beta values
C. The actual and estimated Y values
D. The actual and estimated alpha values
E. None
21. If the equation y = 10 + 0.8x was graphed the:
A. Slope would be -10
B. Slope would be +10
C. The slope would be +0.8
D. The intercept would be +0.8
E. The slope would be 10/0.8
22. In the equation y = ß0 + ß1x + u, ß0 is the _____.
A. Dependent variable
D. Constant parameter
B. Independent variable
E. None of the above
C. Slope parameter
23. In the equation Yi = ß0 + ß1xi+ u, Yi is called
A. Parameter
C. Dependent variables
B. Independent variables
D. Explanatory variable
24. Below you are given a summary of the output from simple linear regression analysis from
the sample of size 15, RSS =100, TSS = 125. The Coefficient of determination ( 𝑅 2 ) is:
A. 0.56
D. 0.20
B. 0.65
E. None
C. 0.34
25. One of the following statements is not correct
A. F-test and t-test in simple regression have the same result
B. You must accept the null hypothesis if the p-value related to F-test is higher than the
set significance level
C. F-test is used to assess whether there is significant relationship exists between
explanatory variables and a dependent one.
D. All of the above
Part Three : Workout
Q1. A financial analyst wants to find out if there is any relationship between return on fund
YYY and return on market index. Six sample data on fund YYY are given below:
Year
Return on fund YYY
Return on market index
1
2
3
4
5
6
16
35
13
26
18
20
12
22
11
14
11
15
Required: Use the above sample data to answer all the following questions:
A. Develop the regression model
ˆ
B. Compute the OLS estimates ̂ 0 and  1 .
ˆ
C. Interpret ̂ 0 and  1 .
D. Calculate estimates of returns & Errors.
E. What is the equation of the OLS line?
F. Compute 𝑅 2 (the coefficient of determination) and interpret it.
Q2. Distinguish the differences and similarities between the logit and probit models