322 Statistical Methods
regression
equation and
r^2 valueregression
lineFigure 8-7
Fitted
regression
line3 Click the Display Equation on chart and Display R-squared value
on chart checkboxes and then click the Close button.
Excel adds a regression line to the plot along with the regression
equation and R^2 value.
4 Drag the text containing the regression equation and R^2 value to a
point above the plot. See Figure 8-7.The regression equation for the mortality data is y 522 1.7 9512. 3577 x.
This means that for every degree that the annual mean temperature increased
in these regions, the breast cancer mortality index increased by about
2.3577 points.
How would you interpret the constant term in this equation^12 21.795^2?
At fi rst glance, this is the y intercept, and it means that if the mean annual
temperature is 0, the value of the mortality index would be 22 1.7 9 5. Clearly
this is absurd; the mortality index can’t drop below zero. In fact, any mean an-
nual temperature of less than 9.24 degrees Fahrenheit will result in a negative
estimate of the mortality index. This does not mean that the linear equation
is useless, but it means you should be cautious in making any predictions for
temperature values that lie outside the range of the observed data.
The R^2 value is 0.7654. What does this mean? The R^2 value, also known as
the coeffi cient of determination, measures the percentage of variation in the
values of the dependent variable (in this case, the mortality index) that can be
explained by the change in the independent variable (temperature). R^2 values
vary from 0 to 1. A value of 0.7654 means that 76.54% of the variation in