After estimating the model given as p=b1+b2 ulc + e, our estimated values gives us
b1 = 0.002437212
b2 = 1.016404615
Therefore our model will be represented as follows:
P = 0.002437212 + 1.016404615 ulc
We can explain the above estimated model as follows:
If we hold all other factors and given that the level of ulc to be zero then p will be equal to
0.002437212, this is our autonomous value in the model, if we hold all other factors constant and increase the ulc by one unit then p will increase by 1.016404615 units.
The value of our coefficient of determination is equal to 0.999463, the correlation of determination gives us the strength of the relationship that exists between two variables, in our case the value of R squared is very close to the value 1 and this shows that there exists a very strong relationship between the two variables.
Hypothesis testing of whether the cost of unit labour has an effect on the cost of production in the UK, for this case we will state the null and the alternative hypothesis; we will consider the test statistics on the slope of the model or the coefficient of labour cost in the model.
T calculated = 251.6576454
At 98% test level on the t table our critical value is
T critical = 2.45726
Therefore because the t calculated is greater than our t critical we reject the null hypothesis that states that the coefficient of labour is equal to zero, therefore the coefficient of labour cost is statistically significant and for this reason we can conclude that the level of labour cost affects the cost of production.
Estimation of the model
Our estimated values are as follows
B1 = 0.001446256
B2 = 0.980010557
B3 = 0.03165183
Therefore our model will take the following form
P = 0.001446256 + 0.980010557 ulc + 0.03165183 umc
The model specifies that if we hold all other factors constant and increase the level of ulc by one unit then the level of p will increase by 0.980010557 units, if on the other hand we hold all other factors constant and increase the level of umc by one unit then the level of p will increase by 0.03165183 units.
In the two estimated model the level of b2 is different, in pm1 our b2 coefficient was
1.016404615 while for pm2 the b2 level is 0.980010557. for the second equition the coefficient has a lower value and this is attributed to the increase in an explanatory variable, in the first equation there was only one explanatory variable while in our second equation we have two explanatory variable, for this reason the b2 in pm2 is lower because of the reduced error of estimation of a viable model that explains the level of p.
In comparing the two estimated models the best way to check their viability is through test statistics of the estimated parameters, for both equations we test statistical significant of the estimates across various test levels, further constructing the confidence interval of the estimates in both equations and comparing them, the model with most statistically significant parameters would be the best to explain this relationship.
The other way to compare the two is through testing the existence of heteroscedasticity and multi-correlation in the model and also the issue of autocorrelations in the estimated models. The coefficient of correlation would only explain the strength of the relationship between the explanatory variables and not give us the significance of the estimated models.
Hypothesis testing of the significance of b1 and b2
The following table summarises the test statistics:
t critical at 98%
For the autonomous value we accept the null hypothesis and this means it is not statistically significant at 98% test level using the t table, for b2 is is statistically significant because we have rejected the null hypothesis, for b3 it is statistically insignificant because we have accepted the null hypothesis at 985 level.
When testing whether b2+b3 =1 we will have to state the null and alternative hypothesis
H0: b2+b3 -1 =0
Ha: b2+b3 -1 ≠ 0
When we perform the test statistic we reject the null hypothesis, therefore we conclude that b2 and therefore b2 + b3 is not equal to one
By testing the above hypothesis we would like to find out if the level of marginal ulc and marginal umc when summed up is equal to one, in this we are testing whether the two variables are the only variables that determine the value of p, because we have rejected the hypothesis then there are other factors that determine the level of p.
Berndt E (2000) The Practice of Econometrics, McGraw hill, New York
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