Question 1

Which of the following best describes the purpose of a scatter diagram (plot) in statistics?

Accepted Answer

To show the relationship between two quantitative variables

Question 2

In a study examining the relationship between age and total cholesterol, which variable is most appropriately considered the explanatory variable?

Accepted Answer

Age

Question 3

What is the range of possible values for the correlation coefficient $$r$$?

Accepted Answer

$$-1 \leq r \leq 1$$

Question 4

A correlation coefficient of $$r = -0.85$$ indicates which of the following?

Accepted Answer

A strong negative linear relationship

Question 5

Which of the following statements about correlation and causation is correct?

Accepted Answer

Correlation does not imply causation

Question 6

Given the least-squares regression line $$\hat{y} = 194.1 + 1.40x$$, what is the predicted total cholesterol for a 40-year-old woman?

Accepted Answer

$$250.0$$

Question 7

What does the slope of the least-squares regression line represent in the context of predicting cholesterol from age?

Accepted Answer

The average increase in cholesterol for each additional year of age

Question 8

If the correlation coefficient $$r = 0.72$$, how would you describe the relationship between the two variables?

Accepted Answer

Moderately strong positive relationship

Question 9

Which of the following is an example of extrapolation in regression analysis?

Accepted Answer

Predicting cholesterol for a 25-year-old when the data only includes ages 30 and above

Question 10

What is the main criterion used to determine the best-fit line in least-squares regression?

Accepted Answer

Minimizing the sum of the squared residuals

Question 11

Which of the following best describes a lurking variable?

Accepted Answer

A variable that influences both the explanatory and response variables, potentially creating a spurious association

Question 12

If the regression equation is $$\hat{y} = 87 + 2.8x$$, what is the predicted value of $$y$$ when $$x = 10$$?

Accepted Answer

$$115$$

Question 13

Which of the following is NOT a property of the correlation coefficient?

Accepted Answer

It is affected by the units of measurement

Question 14

A scatter plot shows a downward trend from left to right. What can you infer about the correlation coefficient?

Accepted Answer

It is negative

Question 15

Which of the following best describes interpolation in the context of regression?

Accepted Answer

Predicting values within the range of the explanatory variable

Question 16

If a regression line has a y-intercept of $$87$$, what does this value represent?

Accepted Answer

The predicted value of the response variable when the explanatory variable is zero

Question 17

Which of the following scenarios would most likely violate the assumptions of linear regression?

Accepted Answer

The relationship between the variables is curved

Question 18

A researcher finds a correlation of $$r = 0.05$$ between two variables. What does this indicate?

Accepted Answer

No linear relationship

Question 19

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

Accepted Answer

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

Question 20

In the context of the MAT 131 Student Survey, if the correlation between commute time and distance is very strong, what does this imply?

Accepted Answer

As distance increases, commute time tends to increase as well

Scatter Diagrams, Correlation, and Least-Squares Regression: Study Guide

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