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 $$\hat{y} = -212 + 61.9x$$, where $$x is $$the head width (inches) of a bear, what is the best predicted weight (in pounds) for a bear with a head width of 6.5 inches?

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

Q: Given the regression equation $$\hat{y} = 53.7 - 0.0056x$$ for car weights ($$x in $$pounds) and highway fuel consumption ($$y in $$mpg), what is the best predicted value for a car that weighs 2500 lb?

$$\hat{y} = 53.7 - 0.0056 \times 2500 = 39.7$$

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 prove 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 claims there is a 20% chance of answering a question correctly by guessing. What is the probability of answering incorrectly?

Accepted Answer

$$0.80$$

Question 5

If a standard multiple-choice test has 5 answer choices per question, what is the probability of guessing a wrong answer?

Accepted Answer

$$0.80$$

Question 6

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

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 take online courses only?

Accepted Answer

$$0.10 	imes 0.10 = 0.01$$

Question 9

A vaccine trial for flu shows 14 out of 1066 subjects who received the vaccine developed flu, while 95 out of 536 who received placebo developed flu. What is the probability that a randomly selected subject developed flu?

Accepted Answer

$$\frac{14 + 95}{1602} = 0.0679$$

Question 10

Given the regression equation $$\hat{y} = 53.7 - 0.0056x$$ for car weights ($$x in $$pounds) and highway fuel consumption ($$y in $$mpg), what is the best predicted value for a car that weighs 2500 lb?

Accepted Answer

$$\hat{y} = 53.7 - 0.0056 	imes 2500 = 39.7$$

Question 11

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

Accepted Answer

$$1 - 0.3 = 0.7$$

Question 12

A table shows that 23 out of 100 females and 17 out of 100 males write with their left hand. What is the probability that a randomly selected subject is a lefty given they are female?

Accepted Answer

$$\frac{23}{100} = 0.23$$

Question 13

If the probability of randomly selecting a female is $$0.5$$ and the probability of being left-handed is $$0.2$$, what is the probability of selecting a left-handed female (assuming independence)?

Accepted Answer

$$0.5 	imes 0.2 = 0.1$$

Question 14

A study finds a strong linear correlation between mozzarella cheese consumption and the number of civil engineering PhDs awarded. What is the best interpretation?

Accepted Answer

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

Question 15

If the probability of a subject developing flu after receiving a placebo is $$\frac{95}{532}$$, what is this probability as a decimal rounded to four places?

Accepted Answer

$$0.1786$$

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

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