Question

Let X ∼ N(0, 1), ∼ N(0, 1). Let Y = 1.75 + 2X + . Generate 100 samples for (X, Y ). Use the generated data to fit a linear regression. (a) Report the fitted coefficients and intercept. (b) Draw a scatter plot of (X, Y ). Add the fitted line and the real line to the scatter plot with different color.

Using R

Answer 1

All R commands are shown in bold.

Generate 100 samples for (X, Y ).

x = rnorm(100)

e = rnorm(100)
y = 1.75 + 2 * x + e

Use the generated data to fit a linear regression.

model = lm(y~x)
model

Call:
lm(formula = y ~ x)

Coefficients:
(Intercept) x
1.763705 1.997952

(a)

fitted coefficients = 1.997952

intercept = 1.763705

(b)

Scatter plot of (X, Y ) is,

plot(x, y, pch = 16, col = "blue")

Add the fitted line and the real line to the scatter plot with different color.

abline(model, col = "red") #Fitted line

lines(x, 1.75 + 2 *x, col = "green") # Real line