Question

For the data set shown​ below.

x   y
3   4
4   5
5   8
7   12
8   15

Find the estimates of β0 and β1.

β0≈b0=-3.256

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

β1≈b1=2.233

(Round to three decimal places as​ needed.)

(b) Compute the standard​ error, the point estimate for σ.

Se=0.5972

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

​(c) Assuming the residuals are normally​ distributed, determine sb1.

sb1=0.144

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

​(d) Assuming the residuals are normally​ distributed, test H0: β1=0 versus H1: β1≠0 at the α=0.05 level of significance. Use the​ P-value approach.

The​ P-value for this test is

__?__.

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

Answer 1

Using Excel , Data -----> Data Analysis ----> Regression.

Output :

a ) Estimate of = b0 = - 3.256

Estimate of = b1 = 2.233

b ) Standard Error = S_e = 0.5972

c) Standard Error for the slope = S_b1 = 0.144

d )

Hypothesis :

The​ P-value for this test is 0.001

Decision about null hypothesis :

Rule : Reject null hypothesis if p-value less than level of significance = 0.05

It is observed that the p-value ( 0.001 ) is less then level of significance ( = 0.05 )

So, Reject Null hypothesis ( )