Question

ANOVA for SLR

source	df	ss	ms	F
regression	1	14.4	14.4	27
Error	3	1.6	0.533333
Total	4	16

R^2=0.9. n=5(there are five x and five y in original table)

1.Construct a 95% confidence interval of B1(beta1),B1(beta1=-1.2)

2.Does the average value of y change with x? Assume a(alpha)=0.05

question 2 is much important plz tell me, thx

Answer 1

1.We have to construct the confidence interval for beta.

The C.I. for beta is (beta+/-margin of error)

ME = critical value * standard error

ME=0.509188*0.5333

Thus C.I. is (-1.47155,-0.92844)

2)Now we have to check significance of beta1

Hypothesis is H₀:beta=0

We reject H₀ if calculated value of t distribution is greater than tabulated value.

Here d.f is n-k-1=5-1-1=3

Thus tabulated value=t_tab=3.18

Calculated value=t_cal=2.25

Thus we accept H_0.i.e.beta1 is not significant.Average value of y does not change with X.

_{​​​​​​}