Q: If the regression line for predicting mpg from weight is $$ \hat{y} = 37.285 - 5.344x $$, what is the predicted mpg for a car weighing 3,000 pounds? (Assume $$ x is in $$thousands of pounds.)

$$ 37.285 - 5.344 \times 3 = 21.253 $$

Q: A regression line is given by $$ \hat{y} = a + bx . If$$ $$ b = 2 $$ and $$ a = 5 $$, what is the predicted value of $$ y $$ when $$ x = 4 $$?

$$ \hat{y} = 5 + 2 \times 4 = 13 $$

Question 1

Which of the following best describes a contingency table?

Accepted Answer

A table that displays frequencies for two categorical variables, with rows and columns representing categories.

Question 2

In the context of association, what is a response variable?

Accepted Answer

The outcome variable on which comparisons are made.

Question 3

Given the following contingency table for meal plan recommendation, what is the conditional proportion of students who recommend a meal plan among those who do NOT have a meal plan?

Have a Meal Plan: No
Recommend: Yes = 51, No = 2, Total = 53

Accepted Answer

$$ \frac{51}{53} \approx 0.96 $$

Question 4

Which of the following statements about the correlation coefficient $$ r  is $$TRUE?

Accepted Answer

Correlation measures the strength and direction of a linear relationship between two quantitative variables.

Question 5

A scatterplot shows a strong negative linear association between weight and miles per gallon (mpg) for cars. Which value of $$ r $$ best represents this relationship?

Accepted Answer

$$ r = -0.87 $$

Question 6

If the regression line for predicting mpg from weight is $$ \hat{y} = 37.285 - 5.344x $$, what is the predicted mpg for a car weighing 3,000 pounds? (Assume $$ x  is in $$thousands of pounds.)

Accepted Answer

$$ 37.285 - 5.344 	imes 3 = 21.253 $$

Question 7

Which of the following is a lurking variable in the association between ice cream sales and car accidents?

Accepted Answer

Population growth

Question 8

What does the squared correlation $$ r^2$ $$ represent in regression analysis?

Accepted Answer

The percent of variability in the response variable explained by the linear relationship with the explanatory variable.

Question 9

If $$ r = -0.87 $$ for the association between mpg and weight, what is $$ r^2$ $$ and what does it mean?

Accepted Answer

$$ r^2$ = 0.7569 $$; 75.69% of the variation in mpg is explained by weight.

Question 10

Which scenario best illustrates Simpson’s Paradox?

Accepted Answer

The direction of association between two variables reverses when a third variable is included in the analysis.

Question 11

A regression line is given by $$ \hat{y} = a + bx . If$$ $$ b = 2 $$ and $$ a = 5 $$, what is the predicted value of $$ y $$ when $$ x = 4 $$?

Accepted Answer

$$ \hat{y} = 5 + 2 	imes 4 = 13 $$

Question 12

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

Accepted Answer

It depends on which variable is the response.

Question 13

In a study of college GPA and high school GPA, which is most likely the explanatory variable?

Accepted Answer

High school GPA

Question 14

Which of the following best describes confounding?

Accepted Answer

Two explanatory variables are both associated with the response variable and with each other.

Question 15

Why is extrapolation considered dangerous in regression analysis?

Accepted Answer

The association given by the regression line may not hold outside the range of sampled $$ x $$ values.

Question 16

Which formula is used to calculate the slope $$ b  of $$the regression line?

Accepted Answer

$$ b = r \left( \frac{s_y}{s_x} \right) $$

Question 17

A regression outlier is defined as:

Accepted Answer

An observation that lies far away from the trend that the rest of the data follows.

Question 18

Which of the following statements about correlation and causation is correct?

Accepted Answer

A strong correlation between $$ x $$ and $$ y $$ does not imply that $$ x $$ causes $$ y  to $$change.

Question 19

Given the regression equation $$ \hat{y} = 37.285 - 5.344x $$, what is the interpretation of the slope $$ -5.344 $$?

Accepted Answer

For each increase of 1 unit (1000 lb) in weight, the predicted mpg decreases by 5.344.

Association Between Variables: Categorical and Quantitative Analysis

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