Question 1

Which of the following best describes the direction, form, and strength of the association in a scatterplot where the points form a tight, upward-sloping line from left to right?

Accepted Answer

Positive, linear, and strong

Question 2

Suppose you are analyzing the relationship between the number of doctors per person and life expectancy in various countries. The correlation is strong, positive, and linear. Which of the following is the best interpretation of this result?

Accepted Answer

There is a strong association, but a lurking variable such as standard of living may explain the relationship.

Question 3

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

Accepted Answer

Categorical Variables Condition

Question 4

Given the regression equation $$\hat{y} = 10.35 + 0.477x$$, what does the slope represent in the context of predicting book price from weight?

Accepted Answer

For each additional ounce in weight, the predicted price increases by $0.477.

Question 5

If the correlation coefficient $$r$$ between two variables is 0.8, what is the value of $$R^2$$ and what does it represent?

Accepted Answer

$$R^2 = 0.64$, which means 64% of the variation in y is explained by the model.

Question 6

Which of the following statements about residuals is TRUE?

Accepted Answer

Residuals are the differences between observed and predicted values.

Question 7

A residual plot for a linear regression model shows a clear curved pattern. What does this indicate?

Accepted Answer

The linear model is inappropriate for the data.

Question 8

Which of the following is the formula for the correlation coefficient $$r$$ using standardized values?

Accepted Answer

$$r = \frac{\sum (z_x z_y)}{n-1}$$

Question 9

If a regression model has $$R^2 = 0.92$, what does this tell you about the model?

Accepted Answer

92% of the variation in the response variable is explained by the model.

Question 10

Which of the following is a lurking variable in the context of the relationship between number of doctors and life expectancy?

Accepted Answer

Standard of living

Question 11

What is the main advantage of re-expressing variables (e.g., using logarithms) in regression analysis?

Accepted Answer

It can make a nonlinear relationship more linear, allowing the use of regression models.

Question 12

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

Accepted Answer

It is affected by changes in the center or scale of either variable.

Question 13

Suppose the correlation between two variables is zero. What does this imply?

Accepted Answer

There is no linear association between the variables.

Question 14

Which of the following best describes 'regression to the mean'?

Accepted Answer

Predicted values of y are closer to their mean than the corresponding x values are to their mean.

Question 15

Which of the following is the formula for the standard deviation of the residuals, $$s_e$$?

Accepted Answer

$$s_e = \sqrt{\frac{\sum e^2$}{n-2}}$$

Question 16

A student fits a regression line to data and finds that the residuals increase in spread as x increases. What condition is violated?

Accepted Answer

Equal Spread Condition

Question 17

Which of the following is a correct interpretation of the intercept in the regression equation $$\hat{y} = b_0$ + b_1$ x$$?

Accepted Answer

The predicted value of y when x is zero.

Question 18

Why is it important to examine a residual plot after fitting a linear regression model?

Accepted Answer

To check for patterns that indicate the model may not be appropriate.

Question 19

Which of the following is a potential pitfall when interpreting a high $$R^2$$ value?

Accepted Answer

A high $$R^2$$ does not guarantee that the model is appropriate or that the relationship is causal.

Chapter 4: Correlation and Linear Regression – Structured Study Notes

Guida di studio - Domande di pratica

Study guide - Flashcard