Correlation and Regressssion - Agricultural Statistical Data Analysis Using Stata - page 194

300

Fitted values
Weight (gms)

200

100

0

0 10 20 30 40 50 60 70 80 90 100

Bulb Diameter (mm)

2.4
2.2

Lg weight
Fitted values

2

1.8
1.6

1.4

1.5 1.6 1.7 1.8 1.9 2

Lg Diameter

Figure 10.7 Onion bulb diameter and weight data with the original data plotted in the top graph
and the transformed data plotted in the bottom graph.

regress lgweight lgdiameter

Source | SS df MS Number of obs = 30
----------+---------------------------- F( 1, 28) = 3128.25
Model | 3.22008254 1 3.22008254 Prob > F = 0.0000
Residual | .028821921 28 .001029354 R-squared = 0.9911
----------+---------------------------- Adj R-squared = 0.9908
Total | 3.24890446 29 .112031188 Root MSE = .03208

Although the results are similar with a significant linear function, the
second table has an R 2 value of 0.9911, which is higher than in the
first table and the y-intercept is closer to 0 at -2.486792. Because the
analysis was done on transformed data, the results are the linear equa-
tion y = 2.511754 x - 2.486792. This should be transformed back to
the original units by taking the antilog of this equation, which is y =
x 2.511754 + 0.00325993. The antilog of the constant -2.486792 is found
by raising 10 to the power of this value. In Stata, if you had used
natural logarithms for the transformation, the inverse of this would
be exp() . Finally, enter the following command to graph the original
data points with the new equation: