 # Confidence and Prediction Intervals

How does the R compute the confidence/predictions intervals?
I can't get the same values with a t-student in Excel. I think the diference is in the residual variance. I would like to know how the R calculate it?

---> predict(model, data, interval = "confidence")
---> predict(model, data, interval = "prediction")

Thank you

Here is a comparison of R's calculation of confidence intervals on a t-test of two 10 element samples to my manual calculation. Check particularly whether Excel uses the adjusted degrees of freedom.

``````n1 <- 10
n2 <- 10

set.seed(3123)
x1 <- rnorm(n1, 0, 1)
x2 <- rnorm(n2, 1, 1)
t.test(x1, x2)
#>
#>  Welch Two Sample t-test
#>
#> data:  x1 and x2
#> t = -2.87, df = 17.109, p-value = 0.01057
#> alternative hypothesis: true difference in means is not equal to 0
#> 95 percent confidence interval:
#>  -1.810749 -0.276839
#> sample estimates:
#>   mean of x   mean of y
#> -0.05637133  0.98742264

#Welch's approx of df
df <- (sd(x1)^2/n1 + sd(x2)^2/n2)^2/((sd(x1)^2/n1)^2/(n1 -1) + (sd(x2)^2/n2)^2/(n2 - 1))
df
#>  17.10865
#critical value of t dist at df
t_crit <- qt(0.975, df)
t_crit
#>  2.108795
#Lower confid value
(mean(x1) - mean(x2)) - t_crit * sqrt(sd(x1)^2/n1 + sd(x2)^2/n2)
#>  -1.810749

#Upper confid value
(mean(x1) - mean(x2)) + t_crit * sqrt(sd(x1)^2/n1 + sd(x2)^2/n2)
#>  -0.276839
``````

Created on 2019-06-01 by the reprex package (v0.2.1)

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