Download Regression

BI 152 Week 12 Sp. 2011
Name __________________________________________
Regression:
When you did your excel graphs on variables from the Class Vital Data, you put in a trend line and the R2
value.
The R2 value is called “R squared” by scientists. It tells how closely the data are clustered around the
trendline, or the strength of the regression. This clustering is a measure of variance or dispersion
around the trend line. (It is similar to, but not identical to standard deviation around the mean.) We call
this measure a regression because of early studies on the heights of fathers and sons. So, if a father was
taller than the mean, his son was likely to be shorter than the father, closer to the mean. If a father was
shorter than the mean, his son was likely to be taller. So we say that the study showed that the sons’
heights regressed toward the mean.
R2 values range from 0 to 1. However, when converted to a percentage , R2 tells what fraction of the
variance is shared by the two variables. Another way to say this is that R2 tells the likelihood of
accurately predicting a Y value for any given X value. So, R2 X 100% = % correlation
Let’s look at some examples:
Heartrates after 30 and 60 seconds of exercise in BI 152 students
What percentage of the variance is shared between the IV (BPM at 30 seconds of exercise) and the DV
(BPM at 60 seconds of exercise)?
At 50 bpm after 30 seconds of exercise, what does the graph predict the corresponding Y value should
be (bpm at 60 seconds)?
What is the chance that you will find the value you just predicted if you test this with a population of BI
152 students?
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BI 152 Week 12 Sp. 2011
Name __________________________________________
Example 2. HR = The taller the height, the more a person weighs
Effect of height on weight of BI 152 students taller than 159 cm.
What is the percentage of shared variance between the variables height and weight?
If a person weighs 80 kg, what does this table predict the height would be?
What is probability that that answer is correct in this population? Explain
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