davidatlarge / compare_model_fits

Compare the fit of multiple polynomal regressions

David Kaiser 2018-09-20

Description

This function fits multiple polynomal regressions to x and y data. The user supplies the highest degree of polynomal that should be included and all polynomals from one to that degree will be calculated. A summary table will be output. ANOVA is performed on consecutive polynomal regressions (e.g. cubic vs quadratic fit) to indicate which increase in polynomal degree still produces a significant reduction in residual sum of squares.

Arguments

• x - a vector of x values
• y - a vector of y values
• degrees - numeric value for the highest degree polynomal
• plot - logical, should the results be plotted? defaults to TRUE

Result

A data frame giving for each polynomal R², the adjusted R², f-statistic value and the p-value of the regression, as well as the Residual Sum of Squares and the ANOVA p-value. A plot showing the data and the different fits (if plot = TRUE).

Example

x <- seq(1,20,length.out = 20)
y <- x^seq(1,2,length.out = 20)
compare_model_fits(x, y, degrees = 5)

##   degree r.squared adj.r.squared f.statistic regression.P        RSS
## 1      1 0.7332036     0.7183815    49.46717 1.457740e-06 177.419625
## 2      2 0.8964548     0.8842730    73.58977 4.252105e-09  68.857543
## 3      3 0.9542187     0.9456347   111.16260 6.309989e-11  30.444554
## 4      4 0.9787035     0.9730244   172.33535 2.418192e-12  14.162166
## 5      5 0.9899925     0.9864185   276.99135 1.766376e-13   6.654959
##        anova.P
## 1           NA
## 2 4.611020e-10
## 3 3.436916e-07
## 4 4.199734e-05
## 5 1.384857e-03