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Can You Guess My IQ?

2.8 Interpreting r2 and se

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What’s the Actual Answer?

A gym teacher was trying to predict the number of chin ups students could do based on how many sit ups they could do.

One student who could do 162 situps had a residual of -5.417 chin ups. What was the actual amount of chin ups that the student could do?

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Talking Structure: Partners

Compare your answer with your partner.

Disagreements?

Sort them out.

A gym teacher was trying to predict the number of chin ups students could do based on how many sit ups they could do.

One student who could do 162 situps had a residual of -5.417 chin ups. What was the actual amount of chin ups that the student could do?

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Big Ideas

  • Interpret the
    • standard error of the residuals (se)
    • r-squared (r2)
  • Use se and r2 to assess how well a least squares regression line models the relationship between two variables.

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There’s Someone Hiding

in the Closet

How tall are they?

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Aquilas

Lindsey

Zac

The New Guy

The Veteran

The Truth Seeker

The Counselors

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Check with your group to make sure your table values are the same.

Do #1 then brainstorm how to do #2 together.

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Mini Debate: Calculating % Improvement

Option 1

Lindsey’s % improvement was 87.68% compared to Aquilas.

Option 2

Lindsey’s % improvement was 812.1% compared to Aquilas.

Which one can you justify mathematically?

Does the method make sense for comparing New Guy’s data to New Guy?

What if you compared the Truth Seeker to the New Guy?

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Calculator Corner

Learn how to calculate regression statistics on your calculators

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Regression Line, r2, r

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Regression Line, r2, r

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Graphing the Data

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Standard Deviation of the Residuals (se)

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Interpretations

Correlation: r

Take the

Then… you know this one!

The correlation coefficient of ______ indicates that there is a (strong, moderate, weak), (positive, negative) linear relationship between (context of y) and (context of x).

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Interpretations

Coefficient of

Determination: r 2

Where have you seen this value before?

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Interpretations

Coefficient of

Determination: r 2

Interpretation for this scenario:

Lindsey’s method of using GPA to predict IQ’s resulted in 87% less error compared to guessing the average IQ for everyone.

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Interpretations

Coefficient of

Determination: r 2

Here’s a generic interpretation

_____ of the variability in (context of y) can be explained by the linear relationship with (context of x).

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What Does This Mean?

87% of the variability in a student’s IQ can be explained by the linear relationship with their GPA.

What about the other 13%?

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Interpretations

Standard Error

of the Residuals: se

Where have you seen this value before?

Or have you?

Think “Standard Deviation”

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Interpretations

Standard Error

of the Residuals: se

Here’s the generic interpretation:

The typical error produced by this model when using (context of x) to predict (context of y) is _____ (units).

Think “Standard Deviation”

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What Does This Mean?

The typical error produced by this model when using GPA to predict IQ is 5.473 points.

Is being off by 5.473 points when predicting IQ okay?

What about 2*se?

What about 3*se?

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With a partner do the following:

Get a computer and Google

Follow these instructions:

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Big Ideas

  • Interpret the
    • standard error of the residuals (se)
    • r-squared (r2)
  • Use se and r2 to assess how well a least squares regression line models the relationship between two variables.