After a series of tests and exploratory analysis, I have design a linear model in R, the model is the following:
summary(gn)
Call:
lm(formula = NA. ~ I(PC^0.25) + I(((PI)^2)), data = DSET)
Residuals:
Min 1Q Median 3Q Max
-425.22 -87.46 -2.30 79.11 396.14
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -2.047e+03 1.094e+02 -18.71 < 2e-16 ***
I(PC^0.25) 1.206e+03 4.231e+01 28.52 < 2e-16 ***
I(((PI)^2)) -5.242e-02 1.233e-02 -4.25 2.81e-05 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 127.2 on 319 degrees of freedom
Multiple R-squared: 0.7475, Adjusted R-squared: 0.746
F-statistic: 472.3 on 2 and 319 DF, p-value: < 2.2e-16
Then, for example, I calculate the interval confidence for a certain input:
> a<-data.frame(PC=58,PI=12)
> a<-predict(gn,newdata=a,interval="prediction",level=0.95)
> a
fit lwr upr
1 1274.515 1022.976 1526.054
Finally, given the coefficients of the model and the same input, I try to calculate the same confidence interval in EXCEL. Using the formula for the 95% interval of each coefficient, <estimate coefficient - 1.96*error, estimate coefficient + 1.96*error>, the fitted value is reasonable but the extremes are far different.
So, the results are : fitted value=1274.499125 , lower=826.5811979 , upper=1722.417051. As you see, the extremes are different from the output of R.
What's my error? What should I do to get the same intervale I got in R?
