Q: Given the regression equation $$\hat{y} = 58.9 - 0.00749x$$, where $$x$$ represents the weight of a car in pounds, what is the predicted highway fuel consumption (in miles per gallon) for a car that weighs 3000 lb?

$$ \hat{y} = 58.9 - 0.00749 \times 3000 = 36.43$$

Q: Given the regression equation $$\hat{y} = -212 + 61.9x$$ for predicting the weight of a bear from its head width $$x$$, what is the best predicted weight for a bear with a head width of 6.5 in?

$$ \hat{y} = -212 + 61.9 \times 6.5 = 190.35$$

Q: Given the regression equation $$\hat{y} = 53.7 - 0.00505x$$ for predicting highway fuel consumption $$y$$ from car weight $$x$$, what is the best predicted value for a car that weighs 2500 lb?

$$ \hat{y} = 53.7 - 0.00505 \times 2500 = 41.075$$

Question 1

Suppose a study finds a strong linear correlation between the concentration of carbon dioxide ($$\mathrm{CO}_2) in $$the atmosphere and the global mean temperature. Does this necessarily mean that changes in $$\mathrm{CO}_2$$ cause changes in global mean temperature? Why or why not?

Accepted Answer

No, because a strong correlation does not imply causation; there could be other variables involved.

Question 2

Given the regression equation $$\hat{y} = 58.9 - 0.00749x$$, where $$x$$ represents the weight of a car in pounds, what is the predicted highway fuel consumption (in miles per gallon) for a car that weighs 3000 lb?

Accepted Answer

$$
\hat{y} = 58.9 - 0.00749 	imes 3000 = 36.43$$

Question 3

Which of the following is the correct formula for the Pearson correlation coefficient $$r$$?

Accepted Answer

$$
r = \frac{n(\Sigma xy) - (\Sigma x)(\Sigma y)}{\sqrt{n(\Sigma x^2$) - (\Sigma x)^2$} \sqrt{n(\Sigma y^2$) - (\Sigma y)^2$}}
$$

Question 4

A psychologist tells you that in an ESP experiment, there is a 20% chance of answering a question correctly. What is the probability of answering incorrectly?

Accepted Answer

$$0.80$$

Question 5

If a multiple-choice question has five possible answers and only one is correct, what is the probability of guessing incorrectly?

Accepted Answer

$$0.80$$

Question 6

Given the regression equation $$\hat{y} = -212 + 61.9x$$ for predicting the weight of a bear from its head width $$x$$, what is the best predicted weight for a bear with a head width of 6.5 in?

Accepted Answer

$$
\hat{y} = -212 + 61.9 	imes 6.5 = 190.35$$

Question 7

In a study, the correlation coefficient between bear weight and chest size is $$r = 0.963141$$ with a p-value of $$0.000. $$What does this indicate?

Accepted Answer

There is a strong, statistically significant linear correlation between bear weight and chest size.

Question 8

If two undergraduate students are randomly selected and 10% of all students take online courses only, what is the probability that both students take online courses only?

Accepted Answer

$$0.01$$

Question 9

A vaccine trial has 14 subjects who developed flu after receiving the vaccine and 1056 who did not. What is the probability that a randomly selected subject from the vaccine group developed flu? (Express as a decimal.)

Accepted Answer

$$\frac{14}{14+1056} = 0.013$$

Question 10

Given the regression equation $$\hat{y} = 53.7 - 0.00505x$$ for predicting highway fuel consumption $$y$$ from car weight $$x$$, what is the best predicted value for a car that weighs 2500 lb?

Accepted Answer

$$
\hat{y} = 53.7 - 0.00505 	imes 2500 = 41.075$$

Question 11

If the probability of an event $$A is$$ $$0.3$$, what is the probability of its complement $$A'$$?

Accepted Answer

$$0.7$$

Question 12

Suppose the correlation coefficient $$r$$ between two variables is $$0.95. $$Which of the following best describes the relationship?

Accepted Answer

There is a strong positive linear relationship.

Question 13

If a day of the year (not a leap year) is randomly selected, what is the probability that it is the author's birthday?

Accepted Answer

$$\frac{1}{365}$$

Question 14

In a study, the correlation between cheese consumption and civil engineering PhDs awarded is found to be strong and positive. What can you conclude?

Accepted Answer

There is a correlation, but this does not imply that cheese consumption causes more PhDs.

Question 15

If the probability of randomly selecting a female from a group is $$0.4$$ and the probability of selecting a left-handed person is $$0.1$$, what is the probability of selecting a female who is left-handed, assuming independence?

Accepted Answer

$$0.04$$

Question 16

Given the regression equation $$\hat{y} = a + bx$$, what does the slope $$b$$ represent?

Accepted Answer

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

Correlation, Causation, Regression, and Probability – Guided Study Notes

Study Guide - Practice Questions

Study Guide - Flashcards