Multiple Regression

Question 1

What is the date and time of the in-person exam?

Answer 1

29 MAY 9:30am – 11:30 pm

Question 2

What percentage of the overall module mark is the exam worth?

Answer 2

60%

Question 3

What are the two parts of the exam and their respective weights?

Answer 3

Part A (20%): 5 multiple choice questions on theory; Part B (80%): 5 exercises with equations

Question 4

When is the revision session for exam preparation?

Answer 4

Thursday, May 1st, 15:15-17:05 CB 1.11

Question 5

What method is used to find the best-fitting line in regression?

Answer 5

Least squares method

Question 6

What does the correlation coefficient represent?

Answer 6

Strength and direction of linear association between 2 variables

Question 7

What is a positive relationship in correlation?

Answer 7

An increase in X is associated with an increase in Y

Question 8

What is a negative relationship in correlation?

Answer 8

An increase in X is associated with a decrease in Y

Question 9

Define simple linear regression.

Answer 9

Describes the nature and rate of change in the linear relationship between two variables

Question 10

What does regression tell us about the dependent variable (Y)?

Answer 10

How much Y is expected to change on average when X increases by one unit

Question 11

What is the equation for a straight line in regression?

Answer 11

Y = a + b * X

Question 12

What does the term ‘residual’ refer to in regression analysis?

Answer 12

The distance between the data point and the regression line

Question 13

What is the significance of the intercept ‘a’ in the regression equation?

Answer 13

The value of Y when X = 0

Question 14

What does a high R-squared value indicate?

Answer 14

A good fit of the model to the data

Question 15

In multiple regression, what does the equation Y = a + b1X1 + b2X2 + … + bk*Xk represent?

Answer 15

The relationship between multiple predictor variables and the outcome variable

Question 16

What is the purpose of the adjusted R-squared?

Answer 16

Adjusts for the number of variables included in the model

Question 17

What does the coefficient ‘b’ represent in a regression model?

Answer 17

The change in Y when X increases by one unit

Question 18

What is multicollinearity?

Answer 18

When two predictors are strongly correlated, affecting the reliability of the regression estimates

Question 19

What happens when a predictor variable is added to a regression model?

Answer 19

Changes in R-squared, size of ‘b’ coefficients, and significance of ‘b’ coefficients should be checked

Question 20

Fill-in-the-blank: The best fitting line minimizes the sum of the _______.

Answer 20

squared deviations

Question 21

True or False: Correlation is symmetric.

Answer 21

True

Question 22

What is the dependent variable in the example about wealth and corruption?

Answer 22

CPI score (0 to 10; highly corrupt to highly clean)

Question 23

What is the significance of a p-value < 0.05 in regression analysis?

Answer 23

Indicates that the predictor variable is significant

Question 24

What does the term ‘predictor variable’ refer to?

Answer 24

An independent variable that is used to predict the outcome variable

Question 25

What is the relationship between GDP and CPI in the example provided?

Answer 25

Higher GDP is associated with lower levels of perceived corruption

Question 26

What is the effect of a 1 ppt increase in the immunisation rate on infant mortality when GNP is included in the model?

Answer 26

1.122 deaths per thousand live births. ## Footnote This indicates that when controlling for GNP, the relationship between immunisation rates and infant mortality becomes less pronounced.

Question 27

Why is it important to compare countries with the same GNP when analyzing immunisation rates and infant mortality?

Answer 27

To ensure that the relationship observed is not confounded by differences in wealth. ## Footnote Countries with higher immunisation rates are often richer, which can independently affect infant mortality.

Question 28

What happens to the estimated effect of immunisation rate on infant mortality when female illiteracy is included in the model?

Answer 28

The estimated effect falls to 0.514 deaths per thousand live births per 1 ppt increase in immunisation rate. ## Footnote Including female illiteracy accounts for another confounding variable affecting infant mortality.

Question 29

What is multicollinearity in the context of regression models?

Answer 29

It occurs when two predictors are strongly correlated (R > 0.8), requiring one to be dropped from the model. ## Footnote This ensures that the unique effect of each predictor can be accurately measured.

Question 30

What does the Standardised Beta coefficient represent in regression analysis?

Answer 30

It indicates how many standard deviations Y changes when X changes by one of its own standard deviations. ## Footnote This allows for comparison of the effects of different predictors measured in different units.

Question 31

Fill in the blank: A dummy variable in regression is a categorical variable with just ______ values.

Answer 31

two. ## Footnote Typically, these values are 0 and 1, representing two categories.

Question 32

What is the null hypothesis (H0) regarding the effect of male gender on wage in the given example?

Answer 32

Holding education level constant, male gender has NO effect on wage. ## Footnote This serves as a baseline to test against the alternative hypothesis (HA).

Question 33

What was found about student evaluations of teaching with respect to gender?

Answer 33

Male lecturers receive evaluations that are 11.305 percentage points higher than female lecturers of the same age and ethnic background. ## Footnote This suggests a gender bias in student evaluations.

Question 34

What percentage of the variation in student evaluations is accounted for by the model discussed?

Answer 34

19.6%. ## Footnote This indicates that a significant portion of the variation remains unexplained, suggesting other factors influence evaluations.

Question 35

What are some factors that might affect student evaluations beyond the model's variables?

Answer 35

* Actual quality of teaching * Subjective experience of teaching * Time of year * Availability of cookies ## Footnote These factors highlight the complexity of evaluating teaching quality.

Question 36

What is the significance of the coefficient for gender in the multivariate regression results?

Answer 36

It increased from 10.994 to 11.305, indicating a significant effect of male gender. ## Footnote This reflects that gender has a measurable impact on evaluations.

Question 37

What is the purpose of adding categorical variables in a regression model?

Answer 37

To assess the effect of categories such as gender or race on the dependent variable. ## Footnote This allows for a more nuanced understanding of how different groups are evaluated.

Question 38

What is the adjusted R-Square value after adding the age and ethnicity variables to the regression model?

Answer 38

Increased from 0.140 to 0.196. ## Footnote This indicates an improvement in the model's explanatory power.

Question 39

True or False: Standardised Beta coefficients can be used to compare the effects of different predictors measured in different units.

Answer 39

True. ## Footnote They allow for meaningful comparisons by converting effects into standard deviation units.