Q: Given the regression equation $$\hat{y} = 58.9 - 0.00749x$$, where $$x$$ represents the weight of a car in pounds, what is the best predicted value of 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 (CO$$_2) in $$the atmosphere and the global mean temperature. Does this necessarily mean that changes in CO$$_2$$ cause changes in global mean temperature? Why or why not?

Accepted Answer

No, because a strong correlation does not imply causation; there may 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 best predicted value of 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

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

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 a question 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

$$\frac{4}{5}$$

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 about the relationship between these two variables?

Accepted Answer

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

Question 8

If the probability that a randomly selected student takes online courses only is $$0.10$$, what is the probability that two randomly selected students both take online courses only?

Accepted Answer

$$0.10 	imes 0.10 = 0.01$$

Question 9

A table shows the annual per capita consumption of mozzarella cheese and the number of civil engineering PhDs awarded. If a strong linear correlation is found, does this mean that eating more cheese causes more PhDs to be awarded?

Accepted Answer

No, correlation does not imply causation; the relationship may be coincidental.

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 the complement of $$A (i.e$$., $$A'$$)?

Accepted Answer

$$1 - 0.3 = 0.7$$

Question 12

In a vaccine study, 14 out of 1056 subjects who received the vaccine developed the flu. What is the probability that a randomly selected vaccinated subject developed the flu? (Express your answer as a decimal rounded to four places.)

Accepted Answer

$$\frac{14}{1070} \approx 0.0131$$

Question 13

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

Accepted Answer

$$0.4 	imes 0.1 = 0.04$$

Question 14

A regression analysis yields a p-value of $$0.000$$ for the correlation between two variables. What does this indicate about the null hypothesis that there is no linear correlation?

Accepted Answer

Reject the null hypothesis; there is strong evidence of a linear correlation.

Question 15

If 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 16

If the probability of an event $$A is$$ $$0.2$$ and the probability of event $$B is$$ $$0.3$$, and $$A$$ and $$B$$ are independent, what is the probability that both $$A$$ and $$B$$ occur?

Accepted Answer

$$0.2 	imes 0.3 = 0.06$$

Statistics Test #2 Review: Correlation, Regression, and Probability

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