Statistics - 1997 Crops Day Variety Index

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.