MLR & Assumptions

Question 1

What is statistical power?

Answer 1

The probability of detecting a true effect when the effect actually exists

Question 2

Why is reporting only a p-value insufficient?

Answer 2

Because it does not convey the magnitude of the effect or whether the study was adequately powered

Question 3

True / False: A statistically significant result always implies a practically important effect

Answer 3

False

Question 4

What is a Type I error?

Answer 4

Rejecting the null hypothesis when it is actually true (false positive)

Question 5

What values correspond to medium and large effects?

Answer 5

Medium:
𝑑 =0.5

Large:
𝑑 = 0.8

Question 6

Power analysis depends on sample size, α, and _______

Answer 6

Effect size

Question 7

What combination should be reported to strengthen scientific conclusions?

Answer 7

p-value

Effect size

Power analysis / sample size justification

Question 8

True / False: Increasing sample size increases statistical power

Answer 8

True

Question 9

According to Cohen, what is considered a small effect?

Answer 9

d=0.2

Question 10

What is leverage?

Answer 10

An observation with extreme X values

Question 11

Residual = observed value minus ______ value

Answer 11

Predicted (fitted)

Question 12

What is collinearity?

Answer 12

High correlation between independent variables

Question 13

What does a curved pattern in a residual plot indicate?

Answer 13

Violation of linearity

Question 14

True / False: A good residual plot should show a random horizontal band

Answer 14

True

Question 15

When does the intercept have no intrinsic meaning?

Answer 15

When predictors never take the value 0

Question 16

What are residuals in regression?

Answer 16

The unexplained error:

e𝑖 = y𝑖 − ŷ𝑖

Question 17

What does VIF = 1 indicate?

Answer 17

No collinearity among predictors

Question 18

What is multicollinearity?

Answer 18

High correlation among more than two predictors.

Question 19

What is an outlier in regression?

Answer 19

An observation with an extreme Y value.

Question 20

Why are bivariate correlations insufficient to detect multicollinearity?

Answer 20

They cannot capture combined relationships among multiple predictors

Question 21

Why are regression diagnostics essential?

Answer 21

Because valid inference depends on assumptions being met

Question 22

What is the tolerance statistic?

Answer 22

The inverse of VIF; the proportion of variance not explained by other predictors.

Question 23

T/F: Multicollinearity violates OLS assumptions

Answer 23

False — but it makes estimation unreliable.

Question 24

Why should the global F-test be run before individual t-tests?

Answer 24

To control Type I error inflation.

Question 25

T/F: Predictor variables must be completely uncorrelated to run MLR

Answer 25

False — perfect independence is unrealistic, but strong correlation causes problems.

Question 26

What is multiple linear regression?

Answer 26

A method for modeling or predicting a continuous response variable using two or more independent variables with linear relationships

Question 27

T/F: Multiple linear regression always improves model performance.

Answer 27

False — adding predictors can inflate R² without improving predictive value

Question 28

What is the global (omnibus) F-test?

Answer 28

A test of whether any predictor contributes to explaining Y

Question 29

State the hypotheses for the global F-test.

Answer 29

H₀: β₁ = β₂ = … = βₖ = 0 H₁: At least one βⱼ ≠ 0 (for j = 1, …, k)

Question 30

What is a partial regression coefficient?

Answer 30

The effect of a predictor after controlling for all others.

Question 31

T/F: The estimate of 𝜎^2 depends on the model specification

Answer 31

True

Question 32

What does adjusted R² correct for?

Answer 32

The number of predictors in the model.

Question 33

Why is multiple regression preferred over bivariate regression in practice?

Answer 33

It allows adjustment for confounders, improves precision, and better reflects real-world complexity.

Question 34

T/F: Removing an insignificant predictor does not require refitting the model

Answer 34

False

Question 35

Why can regression coefficients flip signs?

Answer 35

Omitted variables, suppression, or multicollinearity.

Question 36

What does higher precision mean?

Answer 36

Smaller variance or standard error

Question 37

In a curvilinear model, quadratic terms are written as ______.

Answer 37

𝑥^2

Question 38

What test compares nested regression models?

Answer 38

Partial F-test

Question 39

Fill in the blank – Partial regression coefficients measure the effect of a predictor ________ controlling for all other predictors

Answer 39

on the dependent variable

Question 40

What is the main advantage of adding predictors in multiple regression?

Answer 40

Improves prediction/explanation by reducing unexplained variance and allowing control of extraneous variables

Question 41

How is precision of a regression coefficient defined?

Answer 41

The inverse of its variance; smaller variance → higher precision.

Question 42

What is suppression in regression?

Answer 42

A variable that increases the predictive power of other variables without being directly related to the dependent variable.

Question 43

What does R² represent in multiple regression?

Answer 43

The proportion of variance in Y explained by the predictors.

Question 44

What is the difference between a confidence interval and a prediction interval?

Answer 44

CI estimates variability in the mean response; PI estimates variability in individual predicted values.

Question 45

Give an example of moderation in regression.

Answer 45

An interaction term: X×W→Y, e.g., diet program * BMI → weight loss.

Question 46

T/F – Confounding is operationally present if: βcrude​ ≠ βadjusted​

Answer 46

True

Question 47

Give an example of mediation in regression.

Answer 47

A causal pathway: X→M→Y, e.g., physical activity → caloric expenditure → weight loss.

Question 48

How is multicollinearity detected?

Answer 48

Using Variance Inflation Factor (VIF) or tolerance. VIF > 10 → high multicollinearity Tolerance = 1/VIF

Question 49

What is the formula for the Variance Inflation Factor (VIF) of a predictor Xj in multiple regression?

Answer 49

VIFj = 1 / (1 - Rj²)