Can You Guess My IQ?
2.8 Interpreting r2 and se
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?
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?
Big Ideas
There’s Someone Hiding
in the Closet
How tall are they?
Aquilas
Lindsey
Zac
The New Guy
The Veteran
The Truth Seeker
The Counselors
Check with your group to make sure your table values are the same.
Do #1 then brainstorm how to do #2 together.
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?
Calculator Corner
Learn how to calculate regression statistics on your calculators
Regression Line, r2, r
Regression Line, r2, r
Graphing the Data
Standard Deviation of the Residuals (se)
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).
Interpretations
Coefficient of
Determination: r 2
Where have you seen this value before?
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.
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).
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%?
Interpretations
Standard Error
of the Residuals: se
Where have you seen this value before?
Or have you?
Think “Standard Deviation”
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”
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?
With a partner do the following:
Get a computer and Google
Follow these instructions:
Big Ideas