$$\hat{y} = 3.2 \times 104 - 55.8 = 277$$

$$\hat{y} = 18.67 - 2.167 \times 6 = 5.67$$

Question 1

Which of the following best describes the relationship between club-head speed and driving distance in Table 1?

Accepted Answer

There is a strong positive linear relationship.

Question 2

Given the regression line $$\hat{y} = 3.2x - 55.8$$ for the golf data, what is the predicted driving distance for a club-head speed of 104 mph?

Accepted Answer

$$\hat{y} = 3.2 	imes 104 - 55.8 = 277$$

Question 3

Which scatterplot pattern corresponds to a correlation coefficient $$r$$ close to $$-1$$?

Accepted Answer

A downward sloping straight line (perfect negative linear relationship).

Question 4

What is the residual for the data point $$(103, 274)$$ given the predicted value $$\hat{y} = 269.3$$?

Accepted Answer

$$274 - 269.3 = 4.7$$

Question 5

Which of the following statements about the coefficient of determination $$R^2 is $$correct?

Accepted Answer

$$R^2$$ measures the proportion of total variation in the response variable explained by the regression line.

Question 6

Why is it not appropriate to use the regression line to predict driving distance for a club-head speed of 120 mph, given the data in Table 1?

Accepted Answer

Because 120 mph is outside the range of observed data, and the linear trend may not continue.

Question 7

Given the regression line $$\hat{y} = 18.67 - 2.167x$$ for Table 2, what is the predicted value of $$y$$ when $$x = 6$$?

Accepted Answer

$$\hat{y} = 18.67 - 2.167 	imes 6 = 5.67$$

Question 8

Which of the following is a key requirement for using a linear regression model, as indicated by a residual plot?

Accepted Answer

The residuals should have constant variance (homoscedasticity).

Question 9

In the context of regression, what does the slope $$b_1$$ represent?

Accepted Answer

The average change in the response variable $$y$$ for each one-unit increase in the explanatory variable $$x.$$

Question 10

Which of the following best describes an influential observation in a bivariate dataset?

Accepted Answer

A data point that, if removed, significantly changes the regression line.

Question 11

What is Simpson’s Paradox?

Accepted Answer

A situation where an association between two variables reverses or disappears when a third variable is considered.

Question 12

Which of the following is a marginal distribution in a contingency table?

Accepted Answer

The frequency or relative frequency distribution of either the row or column variable.

Question 13

If the correlation coefficient $$r = 0.939$$ for a dataset with $$n = 8$$, and the critical value for $$n = 8 is$$ $$0.707$$, what can you conclude?

Accepted Answer

The variables are correlated because $$r \u003e 0.707.$$

Question 14

Which of the following best describes a conditional distribution in a contingency table?

Accepted Answer

The relative frequency of each category of the response variable, given a specific value of the explanatory variable.

Question 15

Which of the following is NOT a valid interpretation of the $$y-$$intercept $$b_0 in a $$regression line?

Accepted Answer

The value of $$\hat{y}$$ when $$x = 0$$, even if $$x = 0 is $$not a reasonable value or there is no data near $$x = 0.$$

Question 16

Which of the following residual plots indicates that a linear model is NOT appropriate?

Accepted Answer

A residual plot with a clear pattern or changing spread.

Question 17

If the correlation coefficient $$r is $$close to zero, which of the following is most likely true?

Accepted Answer

There is no linear relationship between the variables.

Question 18

Which formula correctly calculates the slope $$b_1 of $$the least-squares regression line?

Accepted Answer

$$b_1$$ = \frac{r \cdot s_y}{s_x}$$

Question 19

Which of the following best describes the purpose of a residual plot?

Accepted Answer

To assess whether a linear model is appropriate for the data.

Describing the Relationship Between Two Variables: Correlation, Regression, and Contingency Tables

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