Question

9. Assume that the two variables AHE & AGE are related with each other while observing the following condition:

???? = ?0 + ?1???? + ??

The GRETL estimate on the outcome of the above equation is given as hereunder:

Model 1: OLS, using observations 1-500

Dependent variable: AHE

	Coefficient	Std. Error	t-ratio	p-value
const	−4.66024	4.77501	−0.9760	0.3296
AGE	0.823615	0.159987	5.148	<0.0001

*** Mean dependent var 19.80938
S.D. dependent var 10.44739
Sum squared resid 51712.84
S.E. of regression 10.19024
R-squared 0.050528
Adjusted R-squared 0.048621
F(1, 498) 26.50206
P-value(F) 3.80e-07
Log-likelihood −1869.183
Akaike criterion 3742.365
Schwarz criterion 3750.794
Hannan-Quinn 3745.673
What is the estimated slope of the regression line? Comment about this slope.

10. Test the null hypothesis of ?0 ∶ ?1 = 0 , against the alternative of ?a ∶ ?1 ≠ 0. Deploy (i) the prespecified level of significance approach and (ii) the p-value approach. Make sure you interpret your findings. Consider 5% level of significance on both methods of your testing procedure. (Hint: ?1 is the coefficient of variable “AGE” on the estimated outcome stipulated in activity #09 above.)

Answer 1

The regression line is given as -

AHE_{​​​​i} = ₀ + ₁ ​​​​AGE_{​​​​i} + u_​​​i

AHE_​I = - 4.66024 + 0.823615 AGE_{​​​​i} + u_{​​​​​​​​​​​​i}

A) Thus, the estimated slope is the beta coefficient of variable AGE, that is, 0.823615. Which means that if AGE increased by 1 unit then the average of AHE is increased by 0.823615 unit.

B) The hypotheses are -

H_{​​​​​​0} : ₁ = 0. (Null hypothesis)

H_{​​​​​​A}: ​​​​​​₁   0. (Alternate hypothesis)

It is given that ₁ t-value (calculated) is 5.148, which is more than (tabulated value) 2 (which is rule of thumb for large sample size). Then, reject the Null hypothesis, implies slope coefficient is significant in explaning the dependent variable.

C) Similarly, if p-value is less than level of significance which is 0.025 ((1-0.95) /2) in this case. Then reject the null hypothesis.

It is given that p-value is less 0.0001 then it will be less than 0.025 as well. So, reject the null hypothesis implies AGE is significant in explaning the AHE.