Correlation and Regressssion - Agricultural Statistical Data Analysis Using Stata - page 190

This results in a new variable, taichung , where all the entries for
variety Milfor 6(2) are 0. Then a regression is run with the following
command:
regress yield tiller variety taichung
This results in the following output:
Source | SS df MS Number of obs = 16
---------+------------------------ F( 3, 12) = 53.03
Model | 6709577.4 3 2236525.8 Prob > F = 0.0000
Residual | 506108.351 12 42175.6959 R-squared = 0.9299
---------+------------------------- Adj R-squared = 0.9123
Total | 7215685.75 15 481045.717 Root MSE = 205.37
----------------------------------------------------------------
yield | Coef. Std. Err. t P>|t| [95% Conf. Interval]
---------+------------------------------------------------------
tiller | 4.555356 1.833819 2.48 0.029 .5598086 8.550904
variety |-3622.112 840.8033 -4.31 0.001 -5454.065 -1790.159
taichung | 11.45531 2.784214 4.11 0.001 5.389028 17.52159
_cons | 4242.127 404.0575 10.50 0.000 3361.761 5122.492
----------------------------------------------------------------
Notice in the output that the coefficients for tiller and _ cons
are the same as the regression for variety Milfor 6(2). The coefficient for
variety is the difference between the y -intercepts for the two varieties
(620.014 - 4242.127 = -3622.112). Finally, the taichung coefficient is
the difference in the slopes for variety Taichung Native 1 minus the slope
for variety Milfor 6(2) (16.01067 - 4.555356 = 11.45531). The t value for
taichung , which is 4.11, is a test to see if the slopes of the two varieties
are significantly different and, in this case, they are (P>|t| = 0.001).
Frequently, there will be more data points of Y, the dependent
variable (e.g., in a replicated study), than of the independent vari-
able X. Usually when this occurs the dependent data points are aver-
aged before the regression is calculated. This will eliminate noise or
variability in the analysis. This additional data, however, can be use-
ful. For example, in a variety trial, data will be collected from each
replication. A variety trial is not generally analyzed with regression
because the varieties are individual items, but the added data points
may be helpful in examining other relationships. Load the dataset
Onion Pungency Regression.dta. This is a dataset of onion pungency
(i.e., the measurement of pyruvate as μmoles/gram fresh weight,