Residuals Algebra.

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Presentation transcript:

Residuals Algebra

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

DO NOW

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:

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?

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

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

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

Example Predicted Value: We predicted the height of a person with a shoe length of 12.8 in the previous quiz to be 72.66 in. The Actual: Using the table, the height of this person was 70 inches The Residual: 70 – 72.66 = -2.66

Find all of the residuals for each shoe length:

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.