Q: Given the regression equation $$\hat{y} = 61.4 + 2.4x$$, what is the predicted value of $$y$$ when $$x = 50$$?

$$\hat{y} = 61.4 + 2.4 \times 50 = 181.4$$

Question 1

Which of the following best describes the difference between a response variable and an explanatory variable in a statistical study?

Accepted Answer

The response variable is the variable we are interested in studying, while the explanatory variable is any factor that can influence the response variable.

Question 2

Given the pair: Number of square feet in a house and assessed value of the house. Which is the explanatory variable and which is the response variable?

Accepted Answer

Number of square feet is the explanatory variable; assessed value is the response variable.

Question 3

A contingency table is used to display data for which type of variables?

Accepted Answer

Two categorical variables

Question 4

In a study of binge drinking by gender, 48.6% of males and 40.9% of females reported binge drinking. What does this suggest about the association between gender and binge drinking?

Accepted Answer

There is an association because the proportions are different.

Question 5

Which of the following best describes a marginal proportion in a contingency table?

Accepted Answer

The proportion for each category of the response variable based on the total sample size.

Question 6

Which of the following scatterplots would most likely have a correlation value $$r = -0.9$$?

Accepted Answer

A scatterplot where the points are tightly clustered around a line sloping downward.

Question 7

Given the regression equation $$\hat{y} = 61.4 + 2.4x$$, what is the predicted value of $$y$$ when $$x = 50$$?

Accepted Answer

$$\hat{y} = 61.4 + 2.4 	imes 50 = 181.4$$

Question 8

If the correlation coefficient $$r$$ between two variables is close to zero, what does this indicate?

Accepted Answer

There is little to no linear association.

Question 9

Which of the following is a correct interpretation of the slope in a regression equation $$y = a + bx$$?

Accepted Answer

The slope $$b is $$the amount that $$y$$ changes when $$x$$ increases by one unit.

Question 10

Which of the following is a potential risk when using a regression line to predict $$y$$ values for $$x$$ values outside the observed range of data?

Accepted Answer

Extrapolation, which may lead to unreliable predictions.

Question 11

Suppose the correlation between two variables is $$r = 0.8. $$Which of the following statements is true?

Accepted Answer

There is a strong positive linear association between the variables.

Question 12

Which of the following best describes a residual in regression analysis?

Accepted Answer

The difference between the actual value and the predicted value: $$	ext{Residual} = y - \hat{y}$$

Question 13

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

Accepted Answer

$$r$$ can be greater than $$1 if $$the association is very strong.

Question 14

Which of the following scenarios is most likely to involve a lurking variable?

Accepted Answer

A study finds a strong association between ice cream sales and drowning incidents.

Question 15

Given the regression equation $$y = -2.32 + 26.1x$$, what is the residual if the actual value of $$y is 100 $$and $$x = 4$$?

Accepted Answer

Residual $$= 100 - (-2.32 + 26.1 	imes 4) = 100 - 101.08 = -1.08$$

Question 16

Which of the following best describes $$r^2 (r-$$squared) in regression analysis?

Accepted Answer

$$r^2 is $$the proportion of the variation in the $$y-$$values that is accounted for by the linear relationship with $$x.$$

Question 17

Which of the following is a correct formula for the correlation coefficient $$r$$?

Accepted Answer

$$r = \frac{1}{n-1} \sum \left( \frac{x - \bar{x}}{s_x} \right) \left( \frac{y - \bar{y}}{s_y} \right)$$

Question 18

Which of the following is an example of a positive association?

Accepted Answer

As the number of years of education increases, annual income tends to increase.

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