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Analyzing Residuals and Graphing Linear Relationships

Authored by Anthony Clark

English, Mathematics

9th Grade

CCSS covered

Analyzing Residuals and Graphing Linear Relationships
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10 questions

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1.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

A local gym tracks the number of members over the years. The data shows a linear relationship between the year and the number of members. If the regression equation is $y = 50x + 200$, where $x$ is the number of years since 2010, how many members are expected in 2023?

750

1000

900

850

Tags

CCSS.HSF.LE.B.5

2.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

The same gym wants to analyze how well their regression model predicts actual membership numbers. In 2022, they had 350 members. Calculate the residual for that year using the regression equation from the previous question.

-50

-200

50

100

Tags

CCSS.8.EE.C.8C

3.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

A car rental company finds that the cost of renting a car can be modeled by the equation $y = 30x + 50$, where $y$ is the total cost and $x$ is the number of days rented. Graph this linear relationship and identify the y-intercept and slope.

Slope: 30, Y-intercept: 40

Slope: 20, Y-intercept: 50

Slope: 50, Y-intercept: 30

Slope: 30, Y-intercept: 50

Tags

CCSS.8.EE.B.5

4.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

A student collects data on the number of hours studied and test scores. The regression line is given by the equation $y = 5x + 60$. If a student studies for 4 hours, what is the predicted test score?

80

100

70

90

Tags

CCSS.HSF.LE.B.5

5.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Using the same regression line from the previous question, if the actual test score for the student who studied for 4 hours was 78, what is the residual?

-4

-6

2

10

Tags

CCSS.8.EE.C.8C

6.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

A researcher is studying the relationship between temperature and ice cream sales. The regression equation is $y = 10x + 200$, where $x$ is the temperature in degrees Celsius. If the temperature is 25 degrees, how many ice creams are expected to be sold?

300

500

400

450

Tags

CCSS.HSF.LE.B.5

7.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

In the ice cream sales problem, if the actual sales on that day were 270, calculate the residual. What does this residual indicate about the prediction?

-30

100

-50

0

Tags

CCSS.8.EE.C.8C

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