 # Applied Regression Analysis Theory/numerical part 1 Consider mult...

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{r setup, include=FALSE}
knitr::opts_chunk$set(echo = TRUE)  ## Theory 2$X$=$\begin{bmatrix}
2 & 4 \\
0 & 0 \\
-1 & -2 \\
1 & 2
\end{bmatrix}X^T$=$\begin{bmatrix}
2 & 0 & -1 & 1\\
4 & 0 & -2 & 2
\end{bmatrix}X^TX$=$\begin{bmatrix}
6 & 12 \\
12 & 24
\end{bmatrix}$Inverse is not solvable as it is a singular matrix. {r} x1 = c(2, 0, -1, 1) x2 = c(4, 0, -2, 2) X = cbind(x1, x2) y = c(0,-1,-1,0) df = data.frame(X = cbind(x1, x2), y) fit <- lm(y ~., df)  ## A {r, fig.height=2.5, fig.width=5} dat <- read.table("BODY_FAT.TXT", header = TRUE) df <- dat df$Density <- NULL
fit <- lm(SiriBFperc ~., data = df)


{r, fig.height=2.5, fig.width=5}
plot(hat(model.matrix(fit)), type = "h")


{r, fig.height=2.5, fig.width=6}
par(mfrow=c(1,2))
plot(rstudent(fit), type = "h")
plot(cooks.distance(fit), type = "h")


{r, fig.height=4}
par(mfrow=c(2,2))
plot(fit)
...

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