Question 1

The scatterplot above shows a set of data points (blue dots) and a red dashed line. What does the red dashed line most likely represent?

Accepted Answer

The line of best fit (regression line) for the data

Question 2

Based on the scatterplot and the red dashed line, what can you infer about the relationship between the variables on the x- and y-axes?

Accepted Answer

There is a strong positive linear relationship between the variables

Question 3

Suppose the equation of the red dashed line is $$y = mx + b. If $$the slope $$m is $$positive, what does this indicate about the data?

Accepted Answer

As $$x$$ increases, $$y$$ increases

Question 4

If the equation of the regression line is $$y = 0.9x + 2$$, what is the predicted value of $$y$$ when $$x = 20$$?

Accepted Answer

$$y = 0.9 	imes 20 + 2 = 20$$

Question 5

Which of the following best describes the purpose of fitting a regression line to a set of data points?

Accepted Answer

To model the relationship between two variables and make predictions

Question 6

If the data points in the scatterplot were more widely scattered around the regression line, what would this indicate about the strength of the linear relationship?

Accepted Answer

The linear relationship would be weaker

Question 7

If the regression line in the scatterplot is given by $$y = 1.1x + 3$$, what is the y-intercept of the line, and what does it represent?

Accepted Answer

The y-intercept is $$3$$, representing the predicted value of $$y$$ when $$x = 0$$

Question 8

If you were to calculate the average rate of change between the points $$(10, 12)$$ and $$(20, 21) on $$the regression line, what would it be?

Accepted Answer

$$\frac{21 - 12}{20 - 10} = \frac{9}{10} = 0.9$$

Question 9

Which of the following statements is true about the regression line shown in the scatterplot?

Accepted Answer

It minimizes the sum of the squared vertical distances from the data points to the line

Question 10

Suppose you want to use the regression line to predict a value of $$y$$ for $$x = 30$$, but the data only goes up to $$x = 25. $$What is this type of prediction called?

Accepted Answer

Extrapolation

College Algebra: Chapter 1 & 2 Study Notes

Study Guide - Practice Questions

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