load('pressures.Rdata')
n <- length(pressure$Temp)
X <- matrix(cbind(rep(1, n), pressure$Temp), ncol = 2)
H <- X %*% solve(t(X) %*% X) %*% t(X)
H[12, 12]

## [1] 0.06393448

presslm <- lm(Pressure ~ Temp, data = pressure)
summary(presslm)

## 
## Call:
## lm(formula = Pressure ~ Temp, data = pressure)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.25717 -0.11246 -0.05102  0.14283  0.64994 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept) -81.06373    2.05182  -39.51   <2e-16 ***
## Temp          0.52289    0.01011   51.74   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.2328 on 15 degrees of freedom
## Multiple R-squared:  0.9944, Adjusted R-squared:  0.9941 
## F-statistic:  2677 on 1 and 15 DF,  p-value: < 2.2e-16

sigma <- sum(presslm$resid) / 17
summary(presslm)$sigma

## [1] 0.2328294

presslm$residuals[12]

##        12 
## 0.6499419

2 * (1 - pt(4.18, df = 14))

## [1] 0.0009258681