Question

For the data set shown below, complete parts (a) through (d) below.

X 20 30 40 50 60 Y 98 93 91 85 68 ​

(a) Use technology to find the estimates of beta 0 and beta 1.

beta 0 ~ b 0=_____​(Round to two decimal places as​ needed.)

beta 1 ~ b 1=_____(Round to two decimal places as​ needed.)

(b) Use technology to compute the standard error, the point estimate for o' (o with a little tag on the top)

S e =_____(Round to four decimal places as needed.)

(c) Assuming the residuals are normally distributed, use technology to determine Sb1

Sb1 =_____ (Round to four decimal places as required)

(d) Assuming the residuals are normally distributed, test H0: B1 =0 versus H1:B1 =/ at the a = 0.005 level of significance. Use the P - value approach.

The P - value for this test is _____ (Round to three decimal places as needed.

Answer 1

I have solved this using R

A) b0=114.20

b1= -0.68

B) Se= 5.0200

c) Sb1= 0.1587

D) p- value= 0.023

As p-value> 0.005 so we fail to reject the null hypothesis

R Code-

X=c(20,30,40,50,60)
Y=c(98,93,91,85,68)
Z=lm(Y~X)
Z
S=summary(Z)
S$sigma
S

Output-

Call:
lm(formula = Y ~ X)

Coefficients:
(Intercept)            X  
     114.20        -0.68  

[1] 5.01996

Call:
lm(formula = Y ~ X)

Residuals:
   1    2    3    4    5 
-2.6 -0.8  4.0  4.8 -5.4 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept) 114.2000     6.7350  16.956 0.000447 ***
X            -0.6800     0.1587  -4.284 0.023377 *  
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 5.02 on 3 degrees of freedom
Multiple R-squared:  0.8595,    Adjusted R-squared:  0.8126 
F-statistic: 18.35 on 1 and 3 DF,  p-value: 0.02338