Linear Models - Context

Multiple Choice

Sidney is selling his comic book collection on the Internet. The scatter plot shows how many comic books he has left at the end of each day.

(click the image to make it larger)

WHAT TYPE OF ASSOCIATION IS SHOWN?

• Positive

• Negative

• None

Open Ended

Sidney is selling his comic book collection on the Internet. The scatter plot shows how many comic books he has left at the end of each day.

(click the image to make it larger)

Write a conjecture (conclusion statement) about the association.

Multiple Choice

Sidney is selling his comic book collection on the Internet. The scatter plot shows how many comic books he has left at the end of each day.

(click the image to make it larger)

Which of the following equations represents the line of best fit (trend line)?

• $$y=-20x+85$$

• $$y=-10x+90$$

• $$y=10x+90$$

Open Ended

Sidney is selling his comic book collection on the Internet. The scatter plot shows how many comic books he has left at the end of each day.

(click the image to make it larger)

Use the equation to make a conjecture about the number of comic books he will have at the end of the seventh day.

Multiple Choice

Sage belongs to a bird-watching club. Every two days, she goes out and counts the number of Black-hooded Parakeets she sees. The scatter plot shows the number of parakeets she saw in the past 12 days.

(click the image to make it larger)

WHAT TYPE OF ASSOCIATION IS SHOWN?

• Positive

• Negative

• None

Open Ended

Write a conjecture (conclusion statement) about the association.

Multiple Choice

Which of the following is the most reasonable equation for the line of best fit?

• $$y=\frac{1}{2}x+4$$

• $$y=-2x+3$$

• $$y=\frac{1}{2}x+3$$

Open Ended

Use the equation to make a conjecture about the number of parakeets she saw on the 20th day.

Multiple Select

The scatter plot below shows the number of minutes since several celebrities posted a picture on social media and the number of likes the photo has received.

Select ALL statements that you AGREE with.

•  The equation y = 100x accurately depicts the relationship between number of minutes and number of likes.

• After an hour, a celebrity may expect to receive about 6,000 likes.

• After an hour, a celebrity may expect to receive about 100 likes.

• The equation y = x + 100 accurately depicts the relationship between number of minutes and number of likes.

•  The slope of the line of best fit indicates that for every minute since posting, a photo receives about 100 likes.

Multiple Choice

Which statement is true about the data in the scatter plot to the left?

• As x increases, y tends to increase.

• As x increases, y tends to decrease.

• As x increases, y tends to stay unchanged.

• x and y are unrelated.

Multiple Choice

Which statement is true about the data in the scatter plot to the left?

• As the number of at bats increases, the number of hits decreases.

• As the number of at bats increases, the number of hits increases.

• The number of at bats and number of hits are unrelated.

Multiple Choice

At a restaurant, the customers determine how much they want to leave as a tip. The graph shows the amount of tip that 14 different customers left, based on the amount of their bill.

The linear model that represents the trend has an equation of y = 0.14x + 2.5

What does the 0.14 mean in this context?

• The average tip amount is $0.14.

• On a $1 bill, the tip amount is estimated at $0.14.

• A $1 increase in the bill total is associated with a $0.14 increase in tip amount.

• A $0.14 increase in the bill total is associated with a $1 increase in tip amount.

Multiple Select

After giving a test, a teacher collected the data to determine the relationship between how a student performed on the test and how long the student spent studying.

She found a line of best fit for the data and determined the equation for the line to be y = 0.8x + 59.

Which of the statements are fair conclusions that she can make about her model? Select ALL that apply.

• A student who did not study for the test is predicted to earn a grade of 59 points.

• A student who studied for 59 minutes is predicted to earn a grade of 80 points.

• Each additional minute of study time is associated with an additional 0.8 points on the test.

• Each additional minute of study time is associated with an additional 59 points on the test.

• There is a positive linear relationship between the two variables because as study time increases, the test grades also increase.