Correlation and Simple Regression

Question 1

What is the purpose of the z-test?

Answer 1

Compares the mean of one group to a known population mean

Question 2

What does the t-test compare?

Answer 2

Compares the means of two groups

Question 3

What does ANOVA do?

Answer 3

Compares the means of three or more groups at the same time

Question 4

What is eta squared in the context of ANOVA?

Answer 4

The effect size measure that quantifies how much of the variance in the dependent variable is explained by group differences

Question 5

What does the Chi-square test evaluate?

Answer 5

The association between two categorical variables

Question 6

What does Pearson’s r correlation coefficient assess?

Answer 6

The linear association between two continuous variables

Question 7

What are the three types of relationships between two continuous variables?

Answer 7

• Positive
• Negative
• Absent

Question 8

What does a scatterplot visualize?

Answer 8

The association between two continuous variables

Question 9

What does positive covariance indicate?

Answer 9

The variables increase together

Question 10

What limitation does the correlation coefficient address?

Answer 10

It provides a standardized measure of strength and direction of association

Question 11

What is the range of values for the correlation coefficient?

Answer 11

-1 to +1

Question 12

What does a correlation coefficient of 0.90 to 1.00 indicate?

Answer 12

Very strong positive relationship

Question 13

What is the null hypothesis in correlation tests?

Answer 13

In the population, there is NO statistically significant correlation

Question 14

What is a spurious correlation?

Answer 14

A correlation that is a coincidence or caused by a third variable

Question 15

What are the key criteria to assess causation?

Answer 15

• Acceptable degree of correlation
• Logical chain linking the two variables
• Cause must precede effect
• No third variable explains the observed relationship

Question 16

What is the purpose of linear regression?

Answer 16

To describe the nature of the linear relationship between two variables

Question 17

What does the slope in a regression equation represent?

Answer 17

Change in Y for each single unit change in X

Question 18

What is the general form of a regression equation?

Answer 18

Y = a + bX

Question 19

What does ‘a’ represent in the regression equation?

Answer 19

The intercept

Question 20

What does ‘b’ represent in the regression equation?

Answer 20

The slope (regression coefficient)

Question 21

How is the regression line used?

Answer 21

To predict Y from X based on the covariation in their values

Question 22

What does a perfect correlation look like on a scatterplot?

Answer 22

An exact straight line

Question 23

What happens when you regress earnings on years of schooling?

Answer 23

You predict Y from X based on the covariation in their values

Question 24

What is the significance level commonly used in testing correlations?

Answer 24

1% significance level (𝜶 = .01)

Question 25

Fill in the blank: Correlation ______ causation.

Answer 25

does not equal

Question 26

What is the effect size measure of the Chi-square test?

Answer 26

Phi and Cramer’s V

Question 27

What type of relationship does a scatterplot show?

Answer 27

Both linear and non-linear relationships

Question 28

What type of variables does covariance measure?

Answer 28

Continuous variables

Question 29

What does a negative covariance indicate?

Answer 29

One variable increases when the other decreases

Question 30

What is the formula for calculating Pearson's R?

Answer 30

Standardizes the covariance by dividing it by the product of their standard deviations

Question 31

What is the interpretation of a correlation coefficient of 0.01 to 0.20?

Answer 31

Very weak correlation

Question 32

What is the relationship between independent and dependent variables in regression?

Answer 32

The dependent variable depends on the independent variable

Question 33

What does the regression coefficient indicate?

Answer 33

The expected change in the dependent variable for a one-unit change in the independent variable

Question 34

What does the equation Y = a + bX represent?

Answer 34

It predicts the values of Y based on X using a straight line.

Question 35

At what significance level are the linear effects tested?

Answer 35

1% significance level (α = .01).

Question 36

What does the coefficient 'a' represent in the regression equation?

Answer 36

The predicted rate of infant mortality in a country where no children are immunized against diphtheria (a = 151.85).

Question 37

What does the coefficient 'b' indicate in the regression equation?

Answer 37

'b' indicates how the predicted rate of infant mortality changes with a 1 unit increase in immunization (b = -1.34).

Question 38

What is the meaning of R-squared (R²) in regression analysis?

Answer 38

It measures the strength ('goodness of fit') of the linear regression equation predicting the value of Y from X variables.

Question 39

What range does R-squared (R²) cover?

Answer 39

R-squared ranges from 0 to 1.

Question 40

What does an R-squared value of 0 indicate?

Answer 40

The regression model does not predict the value of Y well; none of the variation in Y can be attributed to variation in X.

Question 41

What does an R-squared value close to 1 indicate?

Answer 41

The regression model predicts the value of Y perfectly.

Question 42

What is the purpose of Simple Regression Analysis?

Answer 42

To predict the values of Y based on X using a straight line.

Question 43

What does the term 'unstandardised Beta Coefficient' refer to?

Answer 43

'b' indicates the predicted change in Y when X changes by 1 unit.

Question 44

Fill in the blank: R-squared is the ______ of Pearson's R correlation between observed and predicted values of Y.

Answer 44

square

Question 45

True or False: A value of R-squared of 1 indicates that all variation in Y is attributable to variation in X.

Answer 45

True