1. Residuals
Algebra

2. I can calculate a residual and use it to interpret a graph.
AIM
I can calculate a residual and use it to interpret a graph.
TOPIC: Analyzing Residuals

3. DO NOW

4. Calculating Best-Fit Lines
Steps on the Calculator
Enter the data into STAT
Go back to STAT hit >
Hit 4 for LinReg(ax + b)
**because it is linear**
Use the “a” and “b” values to calculate the best-fit line
Line of Best Fit:

5. Below is the scatter plot showing this data
Below is the scatter plot showing this data. Why does this best-fit line have a positive slope?

6. Using a Trend Line
Now we know the equation of the best-fit line is:
y = 3.7x
What does 3.7 represent in this situation?
What does 25.3 represent in this situation?

7. Use this line to predict the height of a person with a shoe length of 12.8.

8. Residual = actual y value – predicted y value
RESIDUAL: A residual is essentially how far off the number is from what is expected. It’s a way of showing how far something is from what it “should be.”
The Residual Formula:
Residual = actual y value – predicted y value

9. Example
Predicted Value: We predicted the height of a person with a shoe length of 12.8 in the previous quiz to be in.
The Actual: Using the table, the height of this person was 70 inches
The Residual: 70 – = -2.66

10. Find all of the residuals for each shoe length:

11. Calculate the line of best fit for this data set.
EXIT TICKET: Below is a data set comparing an animal’s gestation time to its longevity
Calculate the line of best fit for this data set.