Question 1

Which of the following best describes a regression line in the context of statistics?

Accepted Answer

A line that minimizes the sum of the squares of the residuals.

Question 2

Given the regression equation $$y = 50 + 20x$$, what is the predicted value of $$y$$ when $$x = 3$$?

Accepted Answer

$$y = 110$$

Question 3

What is a residual in the context of regression analysis?

Accepted Answer

The difference between the observed y-value and the predicted y-value.

Question 4

Which of the following is the correct formula for the slope $$m of $$the regression line?

Accepted Answer

$$m = \frac{\sum (x_i - \overline{x})(y_i - \overline{y})}{\sum (x_i - \overline{x})^2$}$$

Question 5

Suppose the regression equation for predicting carbon dioxide emissions (in millions of metric tons) from GDP (in trillions of dollars) is $$y = 100 + 150x. $$What is the predicted emission when GDP is $$2$$ trillion dollars?

Accepted Answer

$$y = 400$$

Question 6

Why must you verify that the linear correlation between two variables is significant before finding a regression line?

Accepted Answer

Because a regression line is only meaningful if there is a significant linear relationship.

Question 7

If the regression line for a data set is $$y = 5x + 2$$, and the observed value for $$x = 4 is$$ $$y = 30$$, what is the residual for this data point?

Accepted Answer

$$8$$

Question 8

Which point does the regression line always pass through?

Accepted Answer

The point $$(\overline{x}, \overline{y})$$

Question 9

A researcher uses technology to find the regression equation $$y = 3x + 7$$ for a data set. What is the predicted $$y$$ when $$x = 5$$?

Accepted Answer

$$y = 22$$

Question 10

Which of the following best explains why the sum of the residuals squared is minimized in regression analysis?

Accepted Answer

To ensure the regression line is as close as possible to all data points.

Question 11

If the regression equation is $$y = 2x + 5$$ and the mean of $$x is$$ $$4$$, what is the mean of $$y$$?

Accepted Answer

$$13$$

Question 12

Which of the following is NOT a correct step in sketching a regression line?

Accepted Answer

Draw the line through the origin regardless of the data.

Question 13

A regression equation is used to predict the number of hospital admissions based on air pollution levels. This is an example of:

Accepted Answer

Applying regression to a real-world scenario.

Question 14

If the regression equation is $$y = -4x + 12$$, what happens to the predicted $$y as$$ $$x$$ increases?

Accepted Answer

The predicted $$y$$ decreases.

Question 15

Which of the following is a plausible reason for a large residual in a regression analysis?

Accepted Answer

The observed value is far from the predicted value.

Linear Regression: Regression Lines and Prediction in Statistics

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