Question

objective 4-2: understand line of best fit.

1. what type of association does the scatter plot show?

positive linear association

1. which of the following graphs shows a nonlinear association?
2. the graph shows the amount of screen time compared to

the amount of time it takes to fall asleep. predict how long it
would take someone to fall asleep if they had 40 minutes of
screen time?
it would probably take them 25 - 30 mins
to fall asleep.

1. which paired data would likely show a negative correlation? select all that apply.

□ number of years lived and number of birthdays had
■ the number of hours shopping and amount of money in bank account
■ the number of hours studying and test score
□ the amount of hours you run each week and your mile time in phy ed
□ the temperature outside and the amount of ice cream sold

Explanation:

Question 2:

Step1: Recall linear vs nonlinear association

A linear association has points that follow a straight - line trend. A nonlinear association has points that follow a curve or no straight - line trend.

Step2: Analyze each graph

• First graph: Points follow a straight - line (positive slope) trend, so linear.
• Second graph: Points follow a straight - line (negative slope) trend, so linear.
• Third graph: Points are scattered without a straight - line or curve trend (no association), but the fourth graph (the right - most one) has points that follow a curve (U - shaped), so it shows a nonlinear association.

Step1: Identify the line of best fit

The graph has a line of best fit (a straight line) that models the relationship between screen time (x - axis) and time to fall asleep (y - axis).

Step2: Find x = 40 on the x - axis

Locate 40 minutes of screen time on the x - axis (Average Minutes of Screen Time).

Step3: Find the corresponding y - value

Follow the vertical line up to the line of best fit, then horizontally to the y - axis (Average Minutes to Fall Asleep). From the graph, when x = 40, the y - value (time to fall asleep) on the line of best fit is approximately 35 minutes (we can also estimate from the trend: as x increases, y increases. The line has a positive slope, and at x = 40, the predicted value from the line is around 35).

• Number of years lived and number of birthdays had: As years lived increase, birthdays increase (positive correlation), so not negative.
• The number of hours shopping and amount of money in bank account: As shopping hours increase, money in the bank (if spending) decreases (negative correlation).
• The number of hours studying and test score: As study hours increase, test scores generally increase (positive correlation), so not negative.
• The amount of hours you run each week and your mile time in Phy Ed: As running hours increase, mile time (how long to run a mile) decreases (negative correlation, since more running makes you faster, so mile time is less).
• The temperature outside and the amount of ice cream sold: As temperature increases, ice cream sales increase (positive correlation), so not negative.

Answer:

The Right Graph (the fourth graph from the left, showing a U - shaped curve of points)

Question 3: