Question

 

 

Xi	3	12	6	20	14
Yi	55	40	55	10	15

 

 

 

 

B – Compute the Standard Error of the estimate. 

 

Answer 1

Using R we can have the result:

CODE:

x <- c(3,12,6,20,14)
y <- c(55,40,55,10,15)
summary(lm(y~x))

OUTPUT:

> x <- c(3,12,6,20,14)

> y <- c(55,40,55,10,15)

> summary(lm(y~x))

Call:

lm(formula = y ~ x)

Residuals:

1 2 3 4 5

-4 8 5 2 -11

Coefficients:

Estimate Std. Error t value Pr(>|t|)

(Intercept) 68.0000 8.1774 8.316 0.00364 **

x -3.0000 0.6526 -4.597 0.01935 *

---

Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 8.756 on 3 degrees of freedom

Multiple R-squared: 0.8757, Adjusted R-squared: 0.8342

F-statistic: 21.13 on 1 and 3 DF, p-value: 0.01935

So, the standard error of estimate is 8.756.

We can elaborately compute that as follows;

CODE:

y_hat <- 68 - 3* x
y_hat
sqrt(sum((y - y_hat)^2)/3)

OUTPUT:

> y_hat <- 68 - 3* x
> y_hat
[1] 59 32 50 8 26
> sqrt(sum((y - y_hat)^2)/3)
[1] 8.75595

Here we also get same result as 8.75595 8.756.

We use the divisor 3 as df as we have 5 observations and we don't have any population known parameter so we are estimating the population parameters so we have df (5-2)=3