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How to find the degrees of freedom of residual from a regression model in R?
To find the degrees of freedom of residual from a regression model, we can use the function df.residual along with the model object.
For example, if we have a regression model stored in an object called Model then the degrees of freedom of residual for the same model can be found by using the command mentioned below −
df.residual(Model)
Example 1
Following snippet creates a sample data frame −
x1<-rpois(20,2) y1<-rpois(20,10) df1<-data.frame(x1,y1) df1
Output
The following dataframe is created −
x1 y1 1 2 5 2 0 14 3 4 9 4 1 9 5 2 5 6 3 10 7 2 10 8 1 13 9 3 6 10 0 13 11 2 10 12 2 6 13 2 6 14 4 11 15 1 10 16 3 12 17 4 10 18 3 7 19 0 14 20 1 7
To create regression model for data in df1, add the following code to the above snippet −
x1<-rpois(20,2) y1<-rpois(20,10) df1<-data.frame(x1,y1) Model1<-lm(y1~x1,data=df1) summary(Model1)
Output
If you execute all the above given snippets as a single program, it generates the following output −
Call: lm(formula = y1 ~ x1, data = df1) Residuals: Min 1Q Median 3Q Max -4.350 -2.694 0.650 2.416 3.462 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 10.9750 1.1809 9.294 2.72e-08 *** x1 -0.8125 0.4990 -1.628 0.121 --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 Residual standard error: 2.823 on 18 degrees of freedom Multiple R-squared: 0.1284, Adjusted R-squared: 0.07996 F-statistic: 2.651 on 1 and 18 DF, p-value: 0.1208
To find degrees of freedom for residual in model Model1, add the following code to the above snippet −
df.residual(Model1)
Output
If you execute all the above given snippets as a single program, it generates the following output −
[1] 18
Example 2
Following snippet creates a sample data frame −
Response<-rnorm(20) iv1<-rnorm(20,2,0.24) iv2<-rnorm(20,10,2.3) df2<-data.frame(Response,iv1,iv2) df2
The following dataframe is created −
Response iv1 iv2 1 -0.85495077 1.528105 7.705541 2 1.05152113 1.833045 8.553894 3 0.83207179 1.686339 14.282792 4 -0.56286758 1.706313 16.849545 5 2.36207904 2.095680 9.689553 6 -1.83340540 2.576143 9.816262 7 0.60208595 1.940719 8.183135 8 0.85376503 2.132368 11.737135 9 -0.27318666 1.737553 10.880559 10 1.59930686 1.856816 11.051310 11 0.21771933 1.620006 11.755168 12 0.76175494 1.815092 12.406097 13 0.01624025 1.982353 13.062458 14 -0.73307457 2.285373 13.814720 15 0.75039176 1.811981 9.986765 16 0.89032608 1.570384 10.295109 17 -0.60115784 2.179361 9.864406 18 0.49524802 2.114340 11.375692 19 0.19472357 1.249829 12.305074 20 -0.32425762 2.374610 11.766768
To create regression model for data in df2, add the following code to the above snippet −
Response<-rnorm(20) iv1<-rnorm(20,2,0.24) iv2<-rnorm(20,10,2.3) df2<-data.frame(Response,iv1,iv2) Model2<-lm(Response~iv1+iv2,data=df2) summary(Model2)
Output
If you execute all the above given snippets as a single program, it generates the following output −
Call: lm(formula = Response ~ iv1 + iv2, data = df2) Residuals: Min 1Q Median 3Q Max -1.65966 -0.57704 0.04338 0.50260 2.14862 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 2.54391 1.81171 1.404 0.178 iv1 -0.82378 0.69325 -1.188 0.251 iv2 -0.06234 0.10053 -0.620 0.543 Residual standard error: 0.9618 on 17 degrees of freedom Multiple R-squared: 0.09101, Adjusted R-squared: -0.01593 F-statistic: 0.851 on 2 and 17 DF, p-value: 0.4444
To find degrees of freedom for residual in model Model2, add the following code to the above snippet −
df.residual(Model2)
Output
If you execute all the above given snippets as a single program, it generates the following output −
[1] 17
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