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How to find the confidence interval for the predictive value using regression model in R?
The confidence interval for the predictive value using regression model can be found with the help of predict function, we just need to use interval argument for confidence and the appropriate level for that. For example, if we have a model M and the data frame for the values of independent variable is named as newdata then we can use the following syntax for the confidence interval −
predict(M,newdata,se.fit=TRUE,interval="confidence",level=0.95)
Example
Consider the below data frame −
set.seed(1234) x1<-sample(0:10,20,replace=TRUE) y1<-sample(6:10,20,replace=TRUE) df1<-data.frame(x1,y1) df1
Output
x1 y1 1 9 8 2 5 9 3 4 10 4 8 7 5 4 10 6 5 7 7 3 8 8 1 9 9 6 9 10 5 8 11 9 6 12 5 8 13 3 9 14 7 7 15 3 8 16 3 7 17 4 10 18 7 6 19 3 8 20 7 6
Example
M1<-lm(y1~x1,data=df1) summary(M1)
Output
Call: lm(formula = y1 ~ x1, data = df1) Residuals: Min 1Q Median 3Q Max -1.6617 -0.6775 -0.1775 1.0566 1.6611 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 9.6299 0.6342 15.185 1.05e-11 *** x1 -0.3228 0.1155 -2.795 0.012 * --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 Residual standard error: 1.113 on 18 degrees of freedom Multiple R-squared: 0.3026, Adjusted R-squared: 0.2638 F-statistic: 7.809 on 1 and 18 DF, p-value: 0.01198
Creating new data and finding the 95% confidence interval for the fitted values of that data −
Example
newdata_x1<-data.frame(x1=c(5,2,3)) predict(M1,newdata_x1,se.fit=TRUE,interval="confidence",level=0.95) $fit
Output
fit lwr upr 1 8.016138 7.492902 8.539373 2 8.984400 8.078130 9.890670 3 8.661646 7.939804 9.383488
Example
$se.fit
Output
1 2 3 0.2490503 0.4313678 0.3435835
Example
$df
Output
[1] 18
Example
$residual.scale
Output
[1] 1.113487
Finding the 90% confidence interval for the fitted values of that data −
Example
predict(M1,newdata_x1,se.fit=TRUE,interval="confidence",level=0.90) $fit
Output
fit lwr upr 1 8.016138 7.584269 8.448007 2 8.984400 8.236381 9.732419 3 8.661646 8.065850 9.257442
Example
$se.fit
Output
1 2 3 0.2490503 0.4313678 0.3435835
Example
$df
Output
[1] 18
Example
$residual.scale
Output
[1] 1.113487
Finding the 80% confidence interval for the fitted values of that data −
Example
predict(M1,newdata_x1,se.fit=TRUE,interval="confidence",level=0.80) $fit
Output
fit lwr upr 1 8.016138 7.684803 8.347472 2 8.984400 8.410512 9.558288 3 8.661646 8.204546 9.118746
Example
$se.fit
Output
1 2 3 0.2490503 0.4313678 0.3435835
Example
$df
Output
[1] 18
Example
$residual.scale
Output
[1] 1.113487
Finding the 75% confidence interval for the fitted values of that data −
Example
predict(M1,newdata_x1,se.fit=TRUE,interval="confidence",level=0.75) $fit
Output
fit lwr upr 1 8.016138 7.720089 8.312187 2 8.984400 8.471628 9.497172 3 8.661646 8.253224 9.070068
Example
$se.fit
Output
1 2 3 0.2490503 0.4313678 0.3435835
Example
$df
Output
[1] 18
Example
$residual.scale
Output
[1] 1.113487
Finding the 99% confidence interval for the fitted values of that data −
Example
predict(M1,newdata_x1,se.fit=TRUE,interval="confidence",level=0.99) $fit
Output
fit lwr upr 1 8.016138 7.299261 8.733014 2 8.984400 7.742734 10.226067 3 8.661646 7.672662 9.650631
Example
$se.fit
Output
1 2 3 0.2490503 0.4313678 0.3435835
Example
$df
Output
[1] 18
Example
$residual.scale
Output
[1] 1.113487
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