Question

Q1.

Model 1: OLS, using observations 1-832

Dependent variable: VALUE

	Coefficient	Std. Error	t-ratio	p-value
const	597.865	7.72837	77.36	<0.0001	***
LOT	30.8658	4.64595	6.644	<0.0001	***

Mean dependent var	610.3780		S.D. dependent var	221.7390
Sum squared resid	38795690		S.E. of regression	216.1985
R-squared	0.050492		Adjusted R-squared	0.049348
F(1, 830)	44.13736		P-value(F)	5.54e-11
Log-likelihood	−5652.552		Akaike criterion	11309.10
Schwarz criterion	11318.55		Hannan-Quinn	11312.73

2-. For the estimated regression in activity #1 above, provide appropriate interpretations for the estimated

intercept and slope parameters of ?0 and ?1 , respectively.

3- Test, at 5% level of significance, the null hypothesis of ?0 ∶ ?1 = 0 , against a one-side alternative of

?a ∶ ?1 > 0. Deploy (i) the pre-specified level of significance approach and (ii) the p-value approach

Answer 1

The OLS regression model is VALUE = 597.865 + 30.8658*LOT

2-

Interpretation of intercept coefficient: The VALUE on an average takes the value of 597.865, when LOT is zero

Interpretation of slope coefficient: On an average VALUE would increase by 30.8658 when the LOT increases by 1 unit

3 -

(i)

Using a pre-specified level of significance approach

Ho: B1 = 0

Ha : B1 > 0

Conduct the t-test at 5% level of significance

The actual t-statistic is t = (b1 - B1)/SE(b1)

=(30.8658 - 0)/4.64595

=6.644

The degree of freedom = n - 2 = 832 - 2 = 830

The critical t-statistic at 5% level of significance and at 830 degrees of freedom is 1.64

Since the actual t-statistic is greater than the critical t-statistic at a 5% level of significance, the null hypothesis Ho: B1 = 0 is not accepted. Thus, one can conclude that the slope coefficient is greater than 0 at a 5% level of significance.

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(ii)

Using the p-value approach

Ho: B1 = 0

Ha : B1 > 0

The p-value corresponding to the actual t-statistic is <0.0001

The actual p-value is less than a critical p-value of 0.5 under the p-value approach.

Thus, the null hypothesis Ho: B1 = 0 is not accepted. Thus, one can conclude that the slope coefficient is greater than 0 at a pre-specified p-value of 0.05