7.4. Linear Regression Equations http://www.ck12.org
From the line of best fit, the calculated value for Student I’s math test mark is 33.6.
Example C
Determine the correlation coefficient and the coefficient of determination for the linear regression equation that you
found in Example B. Is the linear regression equation a good fit for the data?
The correlation coefficient and the coefficient of determination for the linear regression equation are found the same
way that the linear regression equation is found. In other words, to find the correlation coefficient and the coefficient
of determination, after entering the data into your calculator, press
STAT, go to the CALC menu, and choose LinReg(ax + b). After pressing
ENTERto choose LinReg(ax + b), press
ENTERagain, and you should see the following screen:
You can see thatr, or the correlation coefficient, is equal to 0.9486321738, whiler^2 , or the coefficient of determi-
nation, is equal to 0.8999030012. This means that the linear regression equation is a moderately good fit, but not a
great fit, for the data.
Guided Practice
The data below gives the fuel efficiency of cars with the same-sized engines when driven at various speeds.