Question 1

Which of the following is the correct formula for the least squares regression line in statistics?

Accepted Answer

$$\hat{y} = b_0$ + b_1x$$

Question 2

In the context of regression, what does the slope $$b_1$$ represent?

Accepted Answer

The average change in $$y$$ for a one-unit increase in $$x$$

Question 3

Given the regression equation $$\hat{y} = 220.89 - 7.775x$$, what is the predicted value of $$y$$ when $$x = 7.9$$?

Accepted Answer

$$\hat{y} = 159.5$$

Question 4

Which of the following is NOT a condition that must be checked before using linear regression?

Accepted Answer

Categorical Variables Condition

Question 5

What does the residual for a data point represent in a regression analysis?

Accepted Answer

The difference between the observed $$y$$ and the predicted $$\hat{y}$$

Question 6

If the sum of all residuals in a regression model is zero, what does this indicate?

Accepted Answer

This is always true for least squares regression

Question 7

Which of the following best describes $$R^2 in $$the context of regression?

Accepted Answer

The proportion of the variance in $$y$$ explained by $$x$$

Question 8

A regression model for Burger King menu items gives $$R^2 = 0.5743$. What does this mean?

Accepted Answer

57.43% of the variation in fat is explained by protein

Question 9

Which of the following is a potential danger of extrapolation in regression analysis?

Accepted Answer

Predictions may be inaccurate when $$x is $$outside the range of the original data

Question 10

If a regression analysis yields a p-value for the slope greater than 0.05, what is the appropriate conclusion?

Accepted Answer

There is not enough evidence to conclude a statistically significant linear relationship

Question 11

Which variable should be the explanatory (predictor) variable in a regression of 'Annual Salary vs. Years of Service'?

Accepted Answer

Years of Service

Question 12

Given the regression equation $$\hat{y} = 8.4 + 0.91x$$, what is the interpretation of the intercept 8.4 in the context of Burger King menu items?

Accepted Answer

It is the predicted fat content for an item with 0 grams of protein

Question 13

Which of the following is NOT a reason to examine a residual plot after fitting a regression model?

Accepted Answer

To confirm the correlation coefficient

Question 14

If the standard deviation of the residuals ($$s_e) is $$much smaller than the standard deviation of $$y$$ ($$s_y$$), what does this indicate?

Accepted Answer

The regression model explains much of the variation in $$y$$

Question 15

Which of the following best describes the meaning of a negative slope in a regression equation?

Accepted Answer

As $$x$$ increases, $$y$$ tends to decrease

Question 16

Suppose the correlation between two variables is $$r = 0.84. $$What is the value of $$R^2$$?

Accepted Answer

$$R^2 = 0.7056$

Question 17

Which of the following is a correct interpretation of a residual of -14.6 grams of fat for a Burger King menu item?

Accepted Answer

The actual fat content is 14.6 grams less than predicted by the model

Question 18

Which of the following is NOT a valid reason why the y-intercept in a regression equation might be meaningless?

Accepted Answer

The regression line does not pass through the origin

Question 19

Which of the following is true about the sign of the slope $$b_1$$ and the correlation coefficient $$r in a $$regression model?

Accepted Answer

They always have the same sign

Question 20

If a regression analysis is performed on two fair spinners and the p-value for the slope is 0.10, what should you conclude?

Accepted Answer

There is not enough evidence to conclude a statistically significant linear relationship

Linear Regression and Correlation: Understanding and Applying the Least Squares Method

Study Guide - Practice Questions