Question 1

Given the formula for the least-squares regression line $$\hat{y} = b_1$ x + b_0$, what does b_1$ represent in the context of club-head speed and golf ball distance?

Accepted Answer

$$b_1 is $$the increase in the predicted distance (in yards) for each 1 mph increase in club-head speed.

Question 2

Using the formula $$b_1 = r$$ \frac{S_y}{S_x}$$, which of the following statements is correct?

Accepted Answer

The slope $$b_1 is $$calculated by multiplying the correlation coefficient $$r by $$the ratio of the standard deviation of $$y to $$the standard deviation of $$x.$$

Question 3

In the club-head speed and distance example, why should we not use the regression line to predict the distance for a club-head speed of 140 mph?

Accepted Answer

Because extrapolation beyond the observed range (highest observed speed is 105 mph) may not be accurate.

Question 4

What is the correct interpretation of the y-intercept $$b_0 in $$the regression equation $$\hat{y} = b_1$ x + b_0$?

Accepted Answer

It is the predicted value of $$y$$ when $$x = 0$$, provided that $$x = 0 is a $$reasonable value in the context.

Question 5

Given the club-head speed and distance data in Table 5, if the regression equation is $$\hat{y} = 3.1661x + b_0$, what does the slope 3.1661 mean?

Accepted Answer

For every 1 mph increase in club-head speed, the predicted distance increases by 3.1661 yards.

Question 6

If the correlation coefficient $$r$$ between cola consumption and bone mineral density is $$-0.806$$, what is the coefficient of determination $$R^2$$?

Accepted Answer

$$R^2 = 0.650$

Question 7

What does the coefficient of determination $$R^2$$ represent in a regression analysis?

Accepted Answer

The proportion of total variation in the response variable explained by the regression line.

Question 8

In the cola consumption vs. bone mineral density case study, a woman who consumes 4 colas per week has a bone mineral density of 0.873 g/cm². If the predicted value from the regression line for 4 colas per week is 0.875 g/cm², how does her bone mineral density compare to the average?

Accepted Answer

Her bone mineral density is below average for women who consume 4 colas per week.

Question 9

Which of the following is a valid reason to NOT interpret the y-intercept in a regression model?

Accepted Answer

The explanatory variable cannot reasonably be zero.

Question 10

If $$R^2 = 0.947$ for a regression model, what does this mean?

Accepted Answer

94.7% of the variability in the response variable is explained by the regression model.

Question 11

A regression model for bone mineral density predicts values for cola consumption up to 8 cans per week. Would it be appropriate to use this model to predict bone mineral density for a woman who consumes 14 cans per week?

Accepted Answer

No, because this would be extrapolation beyond the observed data range.

Question 12

Which equation correctly calculates the y-intercept $$b_0 of $$the least-squares regression line?

Accepted Answer

$$b_0$$ = \bar{y} - $$b_1$$ \bar{x}$$

Question 13

If the regression equation for club-head speed and distance is $$\hat{y} = 3.1661x + 0$$, and a golfer swings at 103 mph, what is the predicted distance?

Accepted Answer

$$\hat{y} = 3.1661 	imes 103 + 0 = 325.1083$$ yards

Question 14

Which of the following best describes the relationship between club-head speed and driving distance based on the scatter plot and regression line?

Accepted Answer

There is a strong positive linear relationship within the observed range.

Question 15

If the regression line for bone mineral density vs. cola consumption is $$\hat{y} = -0.003x + 0.893$$, what is the predicted bone mineral density for a woman who consumes 6 colas per week?

Accepted Answer

$$\hat{y} = -0.003 	imes 6 + 0.893 = 0.875$$

Question 16

Which scenario is an example of extrapolation in regression analysis?

Accepted Answer

Using the regression model to predict values for explanatory variables outside the observed data range.

Question 17

If $$R^2 = 0.094$ for a regression model, what does this indicate about the model?

Accepted Answer

The regression model explains only 9.4% of the variability in the response variable.

Question 18

Which of the following is NOT a valid interpretation of the slope in a regression equation?

Accepted Answer

The slope represents the predicted value of the response variable when the explanatory variable is zero.

Least-Squares Regression and Coefficient of Determination: Study Notes

Study Guide - Practice Questions

Study Guide - Flashcards