Activity
The scatter plot shows the sale price of several food items, , and the cost of the ingredients used to produce those items, , as well as a line that models the data. The line is also represented by the equation .
What is the predicted sale price of an item that has ingredients that cost $1.50? Be prepared to show your reasoning.
Compare your answer:
$5.98 from the equation , or approximately $6 from the scatter plot graph
What is the predicted ingredient cost of an item that has a sale price of $7? Be prepared to show your reasoning.
Compare your answer:
$1.79 from the equation , or approximately $1.75 from the scatter plot graph
What is the slope of the linear model?
Compare your answer:
3.48.
What does the slope value mean in this situation?
Compare your answer: Your answer may vary, but here is a sample. This means that for every extra dollar spent on ingredients, the sale price of the food item is expected to increase by about $3.48
What is the 𝑦-intercept of the linear model?
Compare your answer:
0.76
What does the value of the -intercept mean in this situation?
Compare your answer: Your answer may vary, but here is a sample. This means that a food item that is made with free ingredients would still be sold for approximately 76 cents.
Does the value of the -intercept make sense in this situation?
Compare your answer: Your answer may vary, but here are some samples.
- This doesn’t seem to make sense because something that is free to make should not cost anything for the customer.
- This might make sense since it would still cost some money to either run the machines or pay the people to make the item.
Video: Using Linear Models
Watch the following video to learn more about how to use linear models.
Self Check
Additional Resources
Interpreting a Linear Model
The scatter plot below shows the height and speed of some of the world’s fastest roller coasters. A line has been drawn to show a good fit for the data.
The equation of the line drawn is .
What does this slope mean in the problem?
For every foot taller the roller coaster is, the speed increases 0.11 miles per hour.
Try it
Try It: Interpreting a Linear Model
Eight students were asked to estimate their score on a 10-point quiz. Their estimated and actual scores are given in the table below. Plot the points. Then sketch a line that fits the data.
Predicted | Actual |
---|---|
6 | 6 |
7 | 7 |
7 | 8 |
8 | 8 |
7 | 9 |
9 | 10 |
10 | 10 |
10 | 9 |
Here are the points from the table plotted on a scatter plot, with the -axis being the predicted scores and the -axis being the actual scores.
Tell what you would expect someone’s grade to actually be if they predicted their grade to be a 5 out of 10.
Compare your answer:
Here is how to answer these questions using the linear model:
Using the linear model above, if a student predicted a 5 on the quiz, they should have an actual score of 6.
What does the slope mean in this problem?
Compare your answer:
Here is how to answer these questions using the linear model:
The slope is the change in the actual grade point for each predicted grade point.