When I try to make prediction and confidence intervals, around a a linear regression model, with two continuous variables and two categorical variables (that may act as dummy variables), results for the two intervals are exactly the same. I'm using the predict() function.
I've already tried with other datasets, that have continuous and discrete variables, but not categorical or dichotomous variables, and intervals are different. I tried removing some variables from the regression model, and the intervals are still the same. On the other hand, I've already compared my data.frame with ones that are exemplified on the R documentation, and I think the problem isn't there.
#linear regression model: modeloReducido
summary(modeloReducido)
> Call: lm(formula = V ~ T * W + P * G, data = Datos)
>
> Residuals:
> Min 1Q Median 3Q Max
> -7.5579 -1.6222 0.3286 1.6175 10.4773
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 0.937674 3.710133 0.253 0.800922
T -12.864441 2.955519 -4.353 2.91e-05 ***
W 0.013926 0.001432 9.722 < 2e-16 ***
P 12.142109 1.431102 8.484 8.14e-14 ***
GBaja 15.953421 4.513963 3.534 0.000588 ***
GMedia 0.597568 4.546935 0.131 0.895669
T:W 0.014283 0.001994 7.162 7.82e-11 ***
P:GBaja -3.249681 2.194803 -1.481 0.141418
P:GMedia -5.093860 2.147673 -2.372 0.019348 *
> --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
>
> Residual standard error: 3.237 on 116 degrees of freedom Multiple
> R-squared: 0.9354, Adjusted R-squared: 0.931 F-statistic: 210 on
> 8 and 116 DF, p-value: < 2.2e-16
#Prediction Interval
newdata1.2 <- data.frame(T=1,W=1040,P=10000,G="Media")
#EP
opt1.PI <- predict.lm(modeloReducido, newdata1.2,
interval="prediction", level=.95)
#Confidence interval
newdata1.1 <- data.frame(T=1,W=1040,P=10000,G="Media")
#EP
opt1.CI <- predict(modeloReducido, newdata1.1,
interval="confidence", level=.95)
opt1.CI
#fit lwr upr
#1 70500.51 38260.24 102740.8
opt1.PI
# fit lwr upr
# 1 70500.51 38260.24 102740.8
opt1.PI and opt1.CI should be different.
The Excel file that I was given out is in the following link: https://www.filehosting.org/file/details/830581/Datos%20Tarea%204.xlsx
