The ministry of transport and communication of a small island Caribbean state is

Question

The ministry of transport and communication of a small island Caribbean state is investigating the determinants of urban transportation by bus. A number of variables were considered for this study. At the conclusion of the study the following variables were selected for the study:

Bustravl-Transportation

Income-Average income per capita

Pop-Population of city (thousands)

Density-Density of city (persons/sq. mile)

Fare-Bus Fare ($, range -)

The dependent variable is BUSTRAVL

Using data from urban areas, OLS was applied using the above variables. Exhibit   shows the results of the OLS regression procedure:

                                                                Model: OLS, using observations 1-40

                                                                Dependent variable:BUSTRAVL

                                                Coefficient          Std. Error             t-ratio                   p-value

Const                                    3111.18                 1071.07                 2.9047                   0.0063   ***

Income                                 -0.202197             0.0625643            -3.2318                 0.0027***

Pop                                        1.58834                 0.122654              12.9497                 <0.0001***

Density                                 0.149027              0.0357127            4.1729                   0.0002***

Fare                                       -295.731               424.835                 -0.6961                 0.4910

Mean dependent var     1933.175              S.D. dependent var         2431.757

Sum squared resid           18480373             S.E of regression               726.6434

R-squared                           0.919868              Adjusted R-squared        0.910710

F(4,35)                                  100.4449              P-Value(F)                          1.12e-18

Log-liklihood                      -317.6243             Akaike criterion                 645.2487

Schwarz criterion              653.6931              Hannan-Quinn                  648.3019

a. Write down the OLS regression estimate

b. What are the assumptions of the OLS model?

c. which variables are statistically significant?

d. Is the overall regression model significant? Give reasons for your answer.

Explanation / Answer

1.The OLS regresion model is

BUSTRAVL=3111.18Const-0.202197Income+1.58834Pop+0.149027 Density-295.731 Fare.

2. The assumptions of OLS model are pretty simplistic. These are

a) The model should be linear in parameters.

b) Errors should be independent and identically normally distributed

c) There should be homoscedasticity i.e. the error variance should be the same.

d) The data should be free from auto correlation.

3.

To check which variables are significant statistically, we need to check their p-values. The p-values which are less than 0.05( the usual level of significance) . R marks the significant variables by adding *'s beside their p-values. So here we see that except for "Fare", every other p-value is less than 0.05. So the significant variables are "Income". "Pop", "Density".

4. To check the overall model's significance, we use F-test. The result of which is noted in 2nd part of the output. Which tests

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