Animal Manure and Mortality Management
Arkansas Swine Odor Survey - Data Analysis
Linear Regression Analysis
An example of the results of a typical regression is given on the following
page. The graph presents how the data is distributed. However, many times
several data points will have the same horizontal and vertical axis values so
several values will appear to be a single value. The graphs also have the
regressed best-fit line. The equation and its associated R Square value are also
indicated.
Below the graph is a summary of the regression statistics. The results
provide several useful pieces of information. The R Square value provides an
estimation of the amount of variability in the dependent variable associated
with the variation in the independent variable. In this example 15.59% of the
variation in the odor measurement is associated with the distance from the odor
source. The R Square can range in value from 0 to 1. A value of 0 would indicate
that the independent variable is not associated with the variation in the
dependent variable. A value of 1 would indicate that the dependent variable
accounts for all the variation in the independent variable.
Comparing the F and Significance F values helps to determine if there is a
statistically significant relationship between the dependent and independent
variables. If the F value is greater than the Significance F, there is a
significant relationship. This is indicated by the F value being in italicized
text and underlined.
There are two probability values that provide insight into the importance of
the factors in the regression equation. If the P-values are less than the a
level of .05, then the factor is statistically significant and is indicated by
underlined italicized text.
If the intercept coefficient is statistically equal to zero, the dependent
variable is equal to zero when the independent variable is equal to zero.
If the coefficient associated with the dependent variable is statistically
significant, then the value of the independent variable is influenced by the
value of the dependent variable.
All Odor = Function
(Distance) |
Regression
Statistics |
| R Square |
0.12592 |
|
|
|
|
| Standard Error |
0.71037 |
|
|
|
|
| Observations |
1129 |
|
|
|
|
| ANOVA |
| |
d f |
S S |
M S |
F |
Significance F |
| Regression |
1 |
81.9296 |
81.9296 |
162.357815 |
7.7070E-35 |
| Residual |
1127 |
568.7112 |
0.5046 |
|
|
| Total |
1128 |
650.6408 |
|
|
|
| |
| |
Coefficients |
Standard Error |
t Stat |
P-value |
|
| Intercept |
3.2551 |
0.1333 |
24.4174 |
4.881E-106 |
|
| ln(dist) |
-0.2661 |
0.0209 |
-12.7420 |
7.707E-35 |
|
| |
| |
Lower 95% |
Upper 95% |
Lower 99.0% |
Upper 99.0% |
|
| Intercept |
2.9935 |
3.5166 |
2.9111 |
3.5990 |
|
| ln(dist) |
-0.3071 |
-0.2251 |
-0.3200 |
-0.2122 |
|
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Arkansas Swine Odor Survey
|
