http://www.ck12.org Chapter 15. Concepts of Statistics
In PreCalculus you will not learn how to calculate the correlation coefficient (you will if you take future statistics
courses!). For now, the calculator will calculate it for you and your job will be to interpret the result. See Example
C.
If the data is sufficiently linear, then your calculator can perform a regression to produce the equation of a line that
attempts to model the trend of the data. The regression line may actually pass through all, some or none of the data
points. This regression line is represented in statistics by:
yˆ=a+bx
The symbol ˆyis pronounced “y-hat” and is the predictedyvalue based on a givenxvalue. Occasionally, you may
also calculate the predictedxvalue given ayvalue, however this is less mathematically sound. Also notice that the
linear regression model is simply a rearrangement of the standard equation of a line,y=mx+b.
Example A
Estimate the correlation coefficient for the following scatterplots.
Solution:
a.r≈0. Because the height(y)does not seem to be dependent on thex, the data is uncorrelated. Another way
to see this is that the slope appears to be undefined.
b.r≈− 0 .7. If the solo point in the bottom left is an outlier, you could choose to not include it in the data. Then,
thervalue would be closer to -1.
c.r≈+ 0 .8. The clump of data seems to be slightly positive correlated and the single point in the upper left has
a strong effect indicating positive slope.
d.r≈− 0 .8. The data seems to be fairly strongly negatively correlated.
e.r≈1. The data seems to be perfectly linearly correlated.Example B
Estimate the regression line through the following scatterplots.