Question 1

Which of the following best describes the main difference between correlation and regression?

Accepted Answer

Regression predicts the value of one variable from another, while correlation only describes the relationship.

Question 2

A psychologist wants to predict a patient's depression score based on the number of stressful life events they have experienced. Which statistical tool should they use?

Accepted Answer

Simple linear regression

Question 3

Given the standardized regression equation $z_\hat{Y} = (r_{XY})(z_X)$, what does $r_{XY}$ represent?

Accepted Answer

The Pearson correlation coefficient between X and Y

Question 4

What is the main idea behind 'regression to the mean'?

Accepted Answer

Extreme scores tend to drift toward the mean over time.

Question 5

If you have a raw score $X$, a mean $M_X$, and a standard deviation $SD_X$, how do you calculate the z-score for $X$?

Accepted Answer

$Z_X = (X - M_X) / SD_X$

Question 6

Which of the following is the correct formula for the regression line in raw scores?

Accepted Answer

$\hat{Y} = a + b(X)$

Question 7

What does the standard error of the estimate represent in regression analysis?

Accepted Answer

The typical distance between the regression line and the actual data points

Question 8

Which of the following best describes the coefficient of determination ($r^2$)?

Accepted Answer

It is the proportion of total error reduced by using the regression line instead of the mean.

Question 9

Suppose you want to predict a student's exam score based on both their hours of study and their attendance rate. Which statistical method should you use?

Accepted Answer

Multiple regression

Question 10

Which of the following is a limitation of regression analysis?

Accepted Answer

Regression analysis is limited when the independent variable is not a scale variable.

Question 11

A researcher finds that the regression line predicts depression scores from stressful life events with a high standard error of the estimate. What does this imply?

Accepted Answer

There is a large amount of variability around the regression line.

Question 12

If the proportionate reduction in error ($r^2$) is 0.60, what does this mean?

Accepted Answer

60% of the variance in the dependent variable is explained by the independent variable.

Question 13

Which step is NOT part of determining the regression equation using z-scores?

Accepted Answer

Multiply the raw score by the mean of Y.

Question 14

In a multiple regression analysis, what does the capitalized $R$ represent?

Accepted Answer

The proportionate reduction in error based on more than one independent variable.

Question 15

A company uses multiple regression to predict sales based on advertising spending and product price. What is a likely benefit of using multiple regression in this context?

Accepted Answer

It allows the company to consider the combined effect of several predictors on sales.

Question 16

Which of the following is the correct formula for calculating the proportionate reduction in error?

Accepted Answer

$r^2 = \frac{SS_{total} - SS_{error}}{SS_{total}}$

Question 17

Why is the regression line called the 'line of best fit'?

Accepted Answer

It minimizes the sum of squared errors between the observed and predicted values.

Question 18

Which real-world scenario best illustrates regression to the mean?

Accepted Answer

A student who scores extremely high on one test tends to score closer to average on the next test.

Chapter 16: Regression – Statistical Prediction and Analysis

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