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Algebra 1

3.6.2 Describing How Two Variables Are Related

Algebra 13.6.2 Describing How Two Variables Are Related

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Activity

Each of the scatter plots shows a strong relationship. Write a sentence or two describing how you think the variables are related.

1. During the month of April, Elena keeps track of the number of inches of rain, or precipitation, recorded for the day and the percentage of people who come to school with rain jackets.

Scatter plot showing a positive correlation between precipitation in inches (x-axis) and percentage of people wearing jackets (y-axis), with a trend line indicating increased jacket use as precipitation rises.

2. A school book club has a list of 100 books for its members to read. They keep track of the number of pages in the books the members read from the list and the amount of time it took to read the book.

Scatter plot showing the relationship between time in hours (x-axis) and number of pages (y-axis). A blue trend line indicates a strong positive correlation as time increases. Data points cluster closely to the line.

3. Number of tickets left for holiday parties at a venue and noise level at the party

Scatter plot showing noise level in decibels (y-axis) versus number of tickets left (x-axis), with a downward trend line indicating noise decreases as more tickets remain.

4. The height and score on a test of vocabulary for several children ages 6 to 13

Scatter plot showing noise level in decibels (y-axis) versus number of tickets left (x-axis), with a downward trend line indicating noise decreases as more tickets remain.

Why Should I Care?

Illustration of a woman in overalls and a headscarf pushing a wheelbarrow with a potted plant and gardening tools outdoors, surrounded by plants and clouds.

One of the most powerful tools you can give a farmer to help improve their crop is statistics. Statistics can help farmers at every stage. For example, seeds are expensive, and if you plant too many strawberries in a market where there are hundreds of strawberry farmers, you might not sell enough to make a profit. With statistical models, farmers can use demand to precisely calculate the proper amount of crops to plant.

Self Check

In this scatter plot, which sentence best describes how the two variables are related?

SCATTER PLOT THAT CAN BE APPROXIMATED BY A LINE, WHERE THE \(y\)-values INCREASE AS THE \(x\)-values INCREASE

  1. As hot dog prices go up, soft drink prices go down.
  2. At different locations, as hot dog prices increase, small soda prices also increase.
  3. Hot dog prices and small soft drink prices are not related.
  4. The more hot dogs that are bought, the more sodas that are bought.

Additional Resources

Causal Relationships

A panel is rating different kinds of potato chips. The scatter plot below shows the relationship between their average rating and the price of the chips, along with the line of best fit. How could the variables be related?

Graph of a scatter plot and its line of best fit on a coordinate plane. The x-axis represents the price of the chips in dollars and the y-axis represents the average number of points the chips were rated.

As the price of a bag of chips in dollars increases, the average rating of the bag of chips in points increases.

Does this represent a causal relationship or simply an association?

In this situation, the independent variable, price, does not seem to cause the rating a person gives the chips. While there appears to be a positive association, there are other factors that may cause the ratings for a bag of chips to go up. For instance, advertising on tv or social media might cause a particular kind of chip to increase in ratings without a change in their price.

Try it

Try It: Describing a Relationship Using a Scatter Plot

Graph of a scatter plot and its line of best fit on a coordinate plane that shows the relationship between the car age in years, which is represented on the x-axis, and the car's mileage in thousands of miles, which is graphed on the y-axis.

The scatter plot shows a strong relationship. How could the variables be related?

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