Question

Find the multiple regression equation for the data given below.

x1 = -2 -2, -1, 2, 2

x2= -3, 1, 0, -2 , 2

y= -6 -11 -4 10 5

The equation is y^=y^=  ++  x1+x1+  x2.

Answer 1

Sol;

use lm function in R to fit a multiple regression

Rcode:

x1 <- c(-2, -2, -1, 2, 2)

x2 <- c(-3, 1, 0, -2 , 2)

y <- c(-6 ,-11, -4 ,10, 5)
model1 <- lm(y~x1+x2)
summary(model1)

Call:
lm(formula = y ~ x1 + x2)

Residuals:
1 2 3 4 5
-0.30000 -0.50000 1.06667 -0.03333 -0.23333

Coefficients:
Estimate Std. Error t value Pr(>|t|)   
(Intercept) -0.8333 0.4014 -2.076 0.17353   
x1 4.2333 0.2186 19.367 0.00266 **
x2 -1.2000 0.2160 -5.555 0.03091 *
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.8756 on 2 degrees of freedom
Multiple R-squared: 0.9947,   Adjusted R-squared: 0.9895
F-statistic: 188.7 on 2 and 2 DF, p-value: 0.005273

From output:

Regression equation

y= -0.8333+ 4.2333x1 -1.2000x2