Question

We have computer output for a SLR model with n=30.

	Estimate	Standard error
(intercept)	12.0	6.00
X	8.0	0.90

1. Find the 95% CI for β​1u​ sing 2.05 as the critical value.
2. Does the evidence suggest a linear relationship between Y and X? Explain.

Answer 1

95 % confidence interval for beta1 (b1)is -

( b1 - t * SEb1) , ( b1 + t * SEb1)

Where SEb1 is standard error of b1 = 0.90

t = 2.05. ( Given)

b1 = 8.0

95% confidence interval for beta1 -

( 8.0 - 2.05 * 0.90) , ( 8.0 + 2.05 * 0.90)

( 6.155 , 9.845 )

B) test statistic is = b1 / SEb1

t stat = 8.0/0.90

t stat = 8.8888

Pvalue = 0.0001

Alpha = 0.05

t critical value is 2.04

Decision - As pvalue less than alpha 0.05 so we Reject the null hypothesis.

Conclusion - as we reject H0 , Hence we say that there is significantly linear relationship between x and y variable.