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: Suppose the regression equation for predicting bear weight from head width is $$\hat{y} = -212 + 61.9x. $$What is the best predicted weight 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 $$\hat{y} = 53.7 - 0.00505x$$ 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

If 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 correlation does not imply causation; other factors or confounding variables may be 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 correctly?

Accepted Answer

$$0.20$$

Question 5

If a standard multiple-choice test question has 5 possible answers and only one is correct, what is the probability of guessing the wrong answer?

Accepted Answer

$$0.80$$

Question 6

Suppose the regression equation for predicting bear weight from head width is $$\hat{y} = -212 + 61.9x. $$What is the best predicted weight 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 cheese consumption and civil engineering PhDs awarded is found to be high. What is the most appropriate interpretation?

Accepted Answer

There is a strong association, but this does not imply that cheese consumption causes more PhDs in civil engineering.

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

$$0.10 	imes 0.10 = 0.01$$

Question 9

A vaccine trial for flu has 14 out of 1060 subjects in the vaccine group develop flu. What is the probability that a randomly selected subject from the vaccine group developed flu? (Express as a decimal rounded to four places.)

Accepted Answer

$$\frac{14}{1060} = 0.0132$$

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 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 12

In a study of left-handedness, 23 out of 217 males and 65 out of 263 females write with their left hand. What is the probability that a randomly selected subject is a female who writes with her left hand?

Accepted Answer

$$\frac{65}{480} = 0.1354$$

Question 13

Which of the following best describes the meaning of the slope in a regression equation predicting fuel consumption from car weight?

Accepted Answer

The slope represents the change in predicted fuel consumption for each additional pound of car weight.

Question 14

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

Accepted Answer

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

Question 15

If the probability of an event $$A is$$ $$0.3$$, what is the probability of the complement of $$A ($$denoted $$A'$$)?

Accepted Answer

$$1 - 0.3 = 0.7$$

Question 16

In a probability experiment, if two events $$A$$ and $$B$$ are independent and $$P(A) = 0.4$$ and $$P(B) = 0.5$$, what is $$P(A \cap B)$$?

Accepted Answer

$$0.4 	imes 0.5 = 0.2$$

Correlation, Causation, and Linear Regression in Statistics

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