Question

For the data set shown​ below

x   y
20   98
30   95
40   91
50   83
60   70

​(a) Use technology to find the estimates of β0 and β1.

β0≈b0=114.60

​(Round to two decimal places as​ needed.)

β1≈b1=-0.68​

(Round to two decimal places as​ needed.)

​(b) Use technology to compute the standard​ error, the point estimate for σ.

Se=__?__

​(Round to four decimal places as​ needed.)

Answer 1

Here I write R-code for given problem as follows

x=c(20,30,40,50,60)
y=c(98,95,91,83,70)
l=lm(y~x)
summary(l)

​​​​​​

And the Output is as follows

Call:
lm(formula = y ~ x)

Residuals:
   1    2    3    4    5 
-3.0  0.8  3.6  2.4 -3.8 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept) 114.6000     5.0675  22.615 0.000189 ***
x            -0.6800     0.1194  -5.693 0.010744 *  
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 3.777 on 3 degrees of freedom
Multiple R-squared:  0.9153,    Adjusted R-squared:  0.887 
F-statistic: 32.41 on 1 and 3 DF,  p-value: 0.01074

From this output  

a) β0≈b0=114.60

β1≈b1=-0.68​

b) point estimate for σ is

Se=3.77