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
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
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