1997 Crops Day Report
R-SQUARE, F-STATISTIC AND T-VALUES
R-squared is a measure of the proportion of the total
variation in the data being studied that is explained by the regression
equation. It is computed by dividing the explained sum of squares by the
total sum of squares. An r-square value of one means the equation explains
all the variation in the data being studied. Another way to look at the
concept of r-square is to know that all regression equations have an often
unwritten term in the equation called the error term. For example the Net
profit equation should be written as:
NET = -UCOP + GROSS + VALUED - MGMTD + error
The calculated r-square for this equation is .76. This number tells us
that the first four terms of the equation describe 76 percent of what is
going on in the flocks studied. The unknown 24 percent is embodied in the
error term and includes the effects of every other variable in net profit.
The f-statistic is another measure of how well the equation
explains the data studied. It is calculated as the mean square due to the
regression divide by the mean square due to the error. If the mean square of
the regression is large relative to the mean square of the error then the
f-statistic will have a large value and the equation fits the data well. In
the net profit equation the f-statistic is 62 indicating the equation has a
good fit to the data.
R-squared and f-statistics measure the value of the equation as a whole.
In addition we need to know if each of the individual parameters in the
equation are important to the end result. T-values measure this. The
t-value measures the probability that an individual parameter is zero. If
the true value of the parameter is zero it does not affect the dependent
variable and thus it does not belong in the equation. All the parameters
studied in this paper have t-values that indicate that they have less than a
5 percent chance of being zero.