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 $$ x is in $$units of 1,000 pounds)

$$ \hat{y} = 37.285 - 5.344 \times 3 = 21.253 $$

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

It always falls between $$ -1 $$ and $$ +1 .$$

Question 5

A scatterplot shows a strong negative linear association between weight and miles per gallon (mpg) of 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 $$ x  is in $$units of 1,000 pounds)

Accepted Answer

$$ \hat{y} = 37.285 - 5.344 	imes 3 = 21.253 $$

Question 7

What does the slope in the regression equation $$ \hat{y} = a + bx $$ represent?

Accepted Answer

The change in the predicted response value for a one-unit increase in the explanatory variable.

Question 8

If $$ r = -0.87 $$ for the association between weight and mpg, what percent of the variation in mpg is explained by the linear relationship with weight?

Accepted Answer

$$ r^2$ = (-0.87)^2$ = 0.7569  or$$ $$ 75.69\% $$

Question 9

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

Accepted Answer

Population growth

Question 10

What is Simpson’s Paradox?

Accepted Answer

When the direction of an association between two variables changes after including a third variable and analyzing at separate levels.

Question 11

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

Accepted Answer

It is resistant to outliers.

Question 12

A regression outlier is best described as:

Accepted Answer

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

Question 13

Which scenario is an example of confounding?

Accepted Answer

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

Question 14

Why is extrapolation using a regression line considered dangerous?

Accepted Answer

There is no guarantee that the association given by the regression line holds outside the range of sampled $$ x $$ values.

Question 15

If a regression line is $$ \hat{y} = 10 + 2x $$ and the observed value at $$ x = 5  is$$ $$ y = 22 $$, what is the residual for this point?

Accepted Answer

$$ 22 - (10 + 2 	imes 5) = 22 - 20 = 2 $$

Question 16

Which of the following best illustrates the difference between correlation and causation?

Accepted Answer

A strong correlation does not necessarily mean that one variable causes the other to change.

Question 17

In a scatterplot, which axis is used for the explanatory variable?

Accepted Answer

Horizontal axis (x-axis)

Question 18

Given the regression equation $$ \hat{y} = a + bx $$, which formula is used to calculate the slope $$ b $$?

Accepted Answer

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

Question 19

Which of the following is a correct interpretation of the y-intercept in a regression equation?

Accepted Answer

The predicted value for $$ y $$ when $$ x = 0 .$$

Question 20

Which of the following is NOT a reason to plot data before performing regression analysis?

Accepted Answer

To ensure the regression line fits all points perfectly.

Chapter 3: Association – Exploring Relationships Between Two Variables

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