Refreshers

Question 1

What is the purpose of studying the relationship between two quantitative variables?

Answer 1

To determine whether the variables are related, the strength and type of the relationship, and whether predictions can be made.

Question 2

A __________ is used to visually display the relationship between two quantitative variables.

Answer 2

Scatterplot

Question 3

True / False: A scatterplot can show direction, form, strength, and outliers in a relationship.

Answer 3

True

Question 4

What does the correlation coefficient (r) measure?

Answer 4

The strength and direction of a linear relationship between two quantitative variables.

Question 5

What is the range of the correlation coefficient r?
A) 0 to 1
B) –∞ to +∞
C) –1 to +1
D) –100 to +100

Answer 5

C

Question 6

True / False: A correlation of r = 0 implies no relationship of any kind between two variables

Answer 6

False (it means no linear relationship)

Question 7

A positive correlation means that as one variable increases, the other variable __________.

Answer 7

Also increases

Question 8

What are the null and alternative hypotheses for a correlation test?

Answer 8

H₀: ρ = 0
H₁: ρ ≠ 0

Question 9

When is the null hypothesis rejected in a correlation test?

Answer 9

When |r| is greater than the critical value.

Question 10

True / False: Correlation implies causation

Answer 10

False

Question 11

Why can combining different subgroups in a dataset produce misleading correlations?

Answer 11

Because relationships within groups can be masked or reversed when data are combined

Question 12

What is linear regression used for?

Answer 12

To model the relationship between variables, describe trends, and make predictions.

Question 13

The regression line is also called the line of __________

Answer 13

Best fit

Question 14

True / False: Regression should be performed even if the correlation is not significant

Answer 14

False

Question 15

What is an independent variable (IV)?

Answer 15

The variable that causes or predicts changes in another variable.

Question 16

What is a dependent variable (DV)?

Answer 16

The variable that is measured as the outcome.

Question 17

In a study on sleep and test scores, which is the IV and which is the DV?

Answer 17

IV: Hours of sleep
DV: Test score

Question 18

One way to identify the DV is to ask which variable occurs __________ in time.

Answer 18

Later

Question 19

What is the strongest evidence for establishing causation?

Answer 19

Experimental evidence with replication.

Question 20

What is the main purpose of linear regression?

Answer 20

To model a linear relationship and make predictions about one quantitative variable from another

Question 21

What method is used to find the regression line?

Answer 21

Least squares

Question 22

What is the “line of best fit”?

Answer 22

The line that best represents the overall trend of the data.

Question 23

Why are regression assumptions important?

Answer 23

Violated assumptions can invalidate the model and its conclusions

Question 24

What is a residual?

Answer 24

The vertical distance between an observed value and its predicted value

Question 25

Name the five key assumptions of linear regression

Answer 25

1. Linearity 2. Normality of residuals 3. Equal variance of residuals (homoscedasticity) 4. Independence of residuals 5. No multicollinearity

Question 26

What type of variable must the dependent variable (DV) be in linear regression?

Answer 26

Continuous

Question 27

True / False: Multicollinearity affects the dependent variable directly

Answer 27

False

Question 28

True / False: Linearity refers to the distribution of the residuals.

Answer 28

False

Question 29

What are residuals in regression?

Answer 29

The differences between observed values and predicted values.

Question 30

Unequal variance of residuals is called __________

Answer 30

Heteroscedasticity

Question 31

What does the normality of residuals assumption require?

Answer 31

Residuals should be approximately normally distributed

Question 32

What is an observed value in regression?

Answer 32

The actual value of the dependent variable collected from data (yᵢ)

Question 33

Can residuals be negative?

Answer 33

Yes, if the predicted value is larger than the observed value (yᵢ – ŷᵢ < 0)

Question 34

What is a predicted value in regression?

Answer 34

The value estimated by the regression model for a given independent variable (ŷᵢ)

Question 35

What is the general form of a multiple linear regression equation?

Answer 35

Where Y = DV, Xs = IVs, βs = coefficients, e = residual 𝑌𝑖 = 𝛽0 + 𝛽1(𝑋1𝑖) + 𝛽2 (𝑋2𝑖) + 𝑒𝑖

Question 36

What is leverage?

Answer 36

Extreme values in independent variable(s) (X) that can disproportionately affect regression results

Question 37

What VIF value indicates no collinearity?

Answer 37

VIF = 1

Question 38

What VIF value often indicates problematic collinearity?

Answer 38

VIF > 10 (though problems can occur with lower values)

Question 39

What is repetitiveness in MLR?

Answer 39

Multiple measures of the same construct included as IVs.

Question 40

T/F: Perfectly correlated IVs (r = 1) cause standard errors to be computable

Answer 40

False — regression fails; matrix cannot be inverted

Question 41

Name three ways to detect collinearity.

Answer 41

1. Large changes in regression coefficients when adding/removing IVs 2. Unexpected signs of coefficients or large standard errors 3. Variance Inflation Factor (VIF)

Question 42

Name two effects of high collinearity on regression results

Answer 42

Misleading significance of IVs (some may appear non-significant) Inflated standard errors of coefficients

Question 43

What is the Variance Inflation Factor (VIF)?

Answer 43

A measure of how much the variance of a regression coefficient is inflated due to collinearity among IVs

Question 44

How are outliers detected?

Answer 44

By examining studentized residuals

Question 45

What is effect size?

Answer 45

A standardized measure of the magnitude of a difference or relationship, independent of sample size

Question 46

How is Type I and Type II error expressed probabilistically?

Answer 46

Type I: 𝑃(Reject H₀ | H₀ true) = 𝛼 Type II: 𝑃(Fail to reject H₀ | H₀ false) = 𝛽

Question 47

How do you calculate Cohen’s d for independent samples?

Answer 47

Cohen's d = (M_2 - M_1) ⁄ SDpooled Where, SDpooled = √((SD_1^2 + SD_2^2) ⁄ 2)

Question 48

Can a “small” effect size still be important?

Answer 48

Yes — even small effects can have practical or cumulative significance, especially in large populations.

Question 48

What is an a priori power analysis?

Answer 48

Estimating the minimum sample size needed to detect a true effect or confirm no significant difference, considering sample size, alpha, and effect size