Question

Q1. Model 1: OLS, using observations 1-832 Dependent variable: VALUE Coefficient Std. Error t-ratio p-value const...

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

Homework Answers

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.

----------------------------------------------------------------------------------------------------------------------------------------------------

(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

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