Q: Given the regression equation $$\hat{y} = 11.61 + 0.215x$$, what is the predicted value of $$y$$ when $$x = 28$$?

$$\hat{y} = 11.61 + 0.215 \times 28 = 17.63$$

Question 1

Which of the following best describes the relationship shown in the scatterplot of cats' age (x-axis) and cats' weight (y-axis)?

Accepted Answer

There is a strong positive linear relationship between age and weight.

Question 2

In a study examining the relationship between hours studied and exam scores, which variable is the explanatory variable?

Accepted Answer

Hours studied

Question 3

Which formula correctly represents the sample linear correlation coefficient $$r$$?

Accepted Answer

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

Question 4

If the correlation coefficient $$r is $$close to $$-1$$, what does this indicate about the relationship between two variables?

Accepted Answer

There is a strong negative linear relationship.

Question 5

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

Accepted Answer

$$r is $$resistant to outliers.

Question 6

Given the regression equation $$\hat{y} = 11.61 + 0.215x$$, what is the predicted value of $$y$$ when $$x = 28$$?

Accepted Answer

$$\hat{y} = 11.61 + 0.215 	imes 28 = 17.63$$

Question 7

Which of the following best describes a lurking variable?

Accepted Answer

A variable that is related to both the explanatory and response variables but is not included in the study.

Question 8

Suppose the correlation coefficient for a sample of size $$n = 10 is$$ $$r = 0.70. $$Using the critical value table, does a significant linear relationship exist at the 5% significance level?

Accepted Answer

Yes, because $$|r| = 0.70 \u003e 0.632 ($$critical value for $$n=10).$$

Question 9

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

Accepted Answer

Correlation does not imply causation.

Question 10

What is the main purpose of finding the least-squares regression line?

Accepted Answer

To minimize the sum of the squared residuals between observed and predicted values.

Question 11

Given the following summary statistics: $$\overline{x} = 26.455$$, $$s_x = 1.0944$$, $$\overline{y} = 17.309$$, $$s_y = 0.235$$, $$r = 0.955$$, what is the slope $$b_1 of $$the least-squares regression line?

Accepted Answer

$$b_1 = r$$ \cdot \frac{s_y}{s_x} = 0.955 \cdot \frac{0.235}{1.0944} = 0.205$$

Question 12

If a scatterplot shows a curved pattern, which of the following is true about using the correlation coefficient $$r$$?

Accepted Answer

You should not use $$r to $$measure the strength of the relationship.

Question 13

Which of the following is the correct formula for the y-intercept $$b_0 of $$the least-squares regression line?

Accepted Answer

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

Question 14

A researcher uses a regression line to predict values for the explanatory variable far outside the range of the observed data. What is this practice called?

Accepted Answer

Extrapolation

Question 15

Which of the following best describes the interpretation of the slope in a regression equation?

Accepted Answer

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

Question 16

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

Accepted Answer

A strong correlation between number of firefighters at a fire and amount of damage caused.

Question 17

If the residual for a data point is positive, what does this mean?

Accepted Answer

The observed value is greater than the predicted value.

Question 18

Which of the following is a correct interpretation of $$r = 0.955$$ for a data set?

Accepted Answer

There is a very strong positive linear relationship between the two variables.

Describing the Relation Between Two Variables: Scatter Diagrams, Correlation, and Least-Squares Regression

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