Measures of the strength of association
of the model.
|
Regression Statistics |
|
|
Multiple R |
0.986987 |
|
R Square |
0.974143 |
|
Adjusted R Square |
0.961214 |
|
Standard Error |
2.51291 |
|
Observations |
7 |
Regression Statistics
|
Interpretation
|
|
| Multiple
R |
0.986987 |
R= Coefficient of
Multiple Correlation = the
positive square root of R-squared |
R Square |
0.974=
97% |
R-squared =
Coefficient of Multiple Determination = percent of the variation in the y-variable that is explained by the
x-variables and the model |
Adjusted R Square |
0.961 |
R-squared
adjusted = version of
R-squared that has been adjusted for the number of predictors in the
model. R-squared tends to
over estimate the strength of the association, especially when more than one independent
variable is included in the model. |
|
Standard Error |
2.51291 |
S = Standard Error = Standard Error of the Estimate = average squared difference of the error in the actual to the predicted values of the date. |
|
Observations |
7 |
Number of observations in the sample |
Model Equation:
|
Coefficients |
|
|
Intercept |
-106.831 |
|
Temperature |
1.538509 |
|
Sun |
5.36558 |
The coefficients for the model are shown below in red. The resulting model is
Water = - 106.83 + 1.54*Temperature + 5.37*Sun
Inferences about the individual coefficients of the model:
We can use the test statistics (t Stat) or the p-values shown in red below, to determine if the variables should be included in the model. At the 10% level, the coefficients for the intercept, temperature and sun are significantly different from zero, since the p-value is less than 0.10. The sun is the only of the variables that is not significant at the 5% level (p=0.054), though its corresponding p-value is very close to 5%. It is left for the reader to decide if they would leave the variable in the model or remove it.
|
Coefficients |
Standard Error |
t Stat |
P-value |
Lower 95% |
Upper 95% |
Lower 95.0% |
Upper 95.0% |
|
|
Intercept |
-106.831 |
11.32667 |
-9.43183 |
0.000705 |
-138.279 |
-75.3833 |
-138.279 |
-75.3833 |
|
Temperature |
1.538509 |
0.125424 |
12.26651 |
0.000254 |
1.190277 |
1.886742 |
1.190277 |
1.886742 |
|
Sun |
5.36558 |
1.986424 |
2.701126 |
0.054031 |
-0.14963 |
10.88079 |
-0.14963 |
10.88079 |
Overall goodness of fit of the model:
The F test statistic (F) and its corresponding p-value (Significance F) certainly indicate an overall goodness of fit for the model. (The p-value (0.000669) is considered highly significant as it is less than 1%.)
|
ANOVA |
||||||
|
df |
SS |
MS |
F |
Significance F |
||
|
Regression |
2 |
951.5983 |
475.7991 |
75.34764 |
0.000669 |
|
|
Residual |
4 |
25.25887 |
6.314719 |
|||
|
Total |
6 |
976.8571 |
||||
Learn the Procedure for Modeling with Indicator Variables
Regression Tutorial Menu Dictionary