Question

I use R to perform the F-test, and got the value below. So, which model is better and how to interpreted the regression model?

Model 1: ELEVATION ~ RIVER + I(caliX^1 * caliY^0) + I(caliX^0 * caliY^1) +
I(caliX^2 * caliY^0) + I(caliX^1 * caliY^1) + I(caliX^0 *
caliY^2)
Model 2: ELEVATION ~ RIVER + I(caliX^1 * caliY^0) + I(caliX^0 * caliY^1) +
I(caliX^2 * caliY^0) + I(caliX^1 * caliY^1) + I(caliX^0 *
caliY^2) + I(caliX^3 * caliY^0) + I(caliX^2 * caliY^1) +
I(caliX^1 * caliY^2) + I(caliX^0 * caliY^3)
Res.Df RSS Df Sum of Sq F Pr(>F)   
1 93 51353
2 89 42840 4 8512.9 4.4214 0.002632 **
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Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Answer 1

For Model 1 :

Residual Degrees of freedom = 93 This is degrees of freedom for Error.

Residual Sum of square = Error sum of square =  51353

As model is not significant none of the other coefficients are present.

For Model 2 :

Residual Degrees of freedom = 89 This is degrees of freedom for Error.

Residual Sum of square = Error sum of square =  42840

Df is degrees of freedom of regression terms = 4

Sum of Sq = Regression sum of square = 8512.9

F statistic =  4.4214

p-value for this model = 0.002632 Which significant at 5% level of significance.

So we can say that 2nd model is significant and better than 1st model.