Q: If you are entering data into a graphing calculator for linear regression, which sequence of buttons should you press first?

$$\\text{STAT} \rightarrow 1: \\text{Edit}$$

Q: If you want to graph the regression line on your calculator after performing linear regression, which step should you take?

Type the regression equation into $$Y_1$$ and press $$\\text{GRAPH}$$

Q: If you want to see all your data points and the regression line on your calculator, which function should you use after entering the data and equation?

$$\\text{ZOOM} \rightarrow 9: \\text{ZoomStat}$$

Q: Which of the following is NOT a step in performing linear regression on a graphing calculator?

Using $$\\text{ZOOM} \rightarrow 6: \\text{ZStandard} to $$calculate the regression

Question 1

Suppose you are given the following data for the number of subscribers (in thousands) to a streaming service over several years:

Year: 2000, 2002, 2004, 2006, 2008, 2010, 2012
Subscribers: 421.36, 507.03, 594.23, 627.81, 682.11, 718.12, 739.99

If you let $$x$$ represent the number of years after 2000, what is the $$x$$ value corresponding to the year 2008?

Accepted Answer

$$x = 8$$

Question 2

You are asked to find the equation of a line that best fits a set of data points that are approximately linear. Which method should you use?

Accepted Answer

Use linear regression on a graphing calculator

Question 3

Given the linear regression equation $$y = 16x + 425.1$$ for a data set where $$x is $$the number of years after 2000, what does the slope $$16$$ represent in the context of the problem?

Accepted Answer

The average increase in subscribers (in thousands) per year

Question 4

If you are entering data into a graphing calculator for linear regression, which sequence of buttons should you press first?

Accepted Answer

$$\text{STAT} ightarrow 1: \text{Edit}$$

Question 5

A data set has $$x$$ values increasing by 2 each time, but the $$y$$ values do not increase by a constant amount. What is the best description of this data?

Accepted Answer

Approximately linear

Question 6

Given the equation $$y = \frac{1}{2}x + 4$$, what is the $$y-$$intercept?

Accepted Answer

$$4$$

Question 7

You are given the points $$(2, 7)$$ and $$(6, 19). $$What is the equation of the line passing through these points in slope-intercept form?

Accepted Answer

$$y = 3x + 1$$

Question 8

After performing linear regression on a data set, you obtain the equation $$y = 8x + 65. $$What is the predicted value of $$y$$ when $$x = 5$$?

Accepted Answer

Question 9

Suppose you have a data set that is exactly linear. What does this mean about the change in $$y$$ for each change in $$x$$?

Accepted Answer

The change in $$y is $$constant for each change in $$x$$

Question 10

If you want to graph the regression line on your calculator after performing linear regression, which step should you take?

Accepted Answer

Type the regression equation into $$Y_1$$ and press $$\text{GRAPH}$$

Question 11

A student enters data into $$L_1$$ and $$L_2 on $$their calculator and performs linear regression, obtaining $$y = 12x + 100. $$What is the predicted $$y$$ value when $$x = 7$$?

Accepted Answer

$$y = 184$$

Question 12

Which of the following best describes the purpose of using linear regression in real-world data analysis?

Accepted Answer

To find the equation of a line that best fits the data points

Question 13

If the regression equation for a data set is $$y = 5x + 20$$, and the actual $$y$$ value for $$x = 4 is$$ $$45$$, what is the residual for this data point?

Accepted Answer

$$5$$

Question 14

A data set shows a steady increase in $$x$$ but the change in $$y is $$not consistent. What should you do to model this data?

Accepted Answer

Use linear regression to find the best fit line

Question 15

You are given the equation $$y = \frac{2}{3}x - 8. $$What is the slope of the line?

Accepted Answer

$$\frac{2}{3}$$

Question 16

If you want to see all your data points and the regression line on your calculator, which function should you use after entering the data and equation?

Accepted Answer

$$\text{ZOOM} ightarrow 9: \text{ZoomStat}$$

Question 17

A company tracks its sales every year and finds the regression equation $$y = 25x + 300$$, where $$x is $$the number of years since 2010. What is the predicted sales value in 2018?

Accepted Answer

Question 18

Which of the following is NOT a step in performing linear regression on a graphing calculator?

Accepted Answer

Using $$\text{ZOOM} ightarrow 6: \text{ZStandard} to $$calculate the regression

Question 19

If a data set is exactly linear, and you calculate the change in $$y$$ for each change in $$x as$$ $$+42$$, what is the slope of the line?

Accepted Answer

$$42$$

Question 20

You are given the equation $$y = \sqrt{2x - 3}. Is $$this equation linear?

Accepted Answer

No, because it contains a square root of $$x$$

Linear Regression and Graphing Calculator Techniques in College Algebra

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