Multiple regression exercise - Coursework Example

Due: Introduction In this study we intended to establish the relationship between the value of Qatar’s exports in the oil and gas sector and the size of Qatar’s economy (as measured by GDP), the size of the economy of the importing country (as measured by GDP) and the distance between Qatar and the importing country. To determine the relationship, we conducted a multiple regression test and the results are shown in the preceding sections below;OutputThe following output was generated from excel;The table below gives the summary output;Goodness of fit statistics:Observations391.

000Sum of weights391.000DF387.000R²0.448Adjusted R²0.444MSE6.273RMSE2.505MAPE13.071DW1.943Cp4.000AIC721.961SBC737.836PC0.563The above table gives the summary statistics from the regression output. The value of R2 is given as 0.448 which means that 44.8% variation in the dependent variable (lnExport) is explained by the independent variables (lnGDPQatar , lnGDPIC and lnDist) in the model. The model explains only 44.8% variation in the dependent variable (lnExport) the other percent (55.2%) is explained by the error term.

Analysis of variance:SourceDFSum of squaresMean squaresFPr > FModel31970.044656.681104.682< 0.0001Error3872427.6886.273Corrected Total3904397.732   Computed against model Y=Mean(Y)The Analysis of Variance (ANOVA) is shown in the table above. The F-value is given as 104.682 while the p-value is 0.0001 |t|Lower bound (95%)Upper bound (95%)Intercept-2.8878.643-0.3340.739-19.88014.105lnGDPQatar1.1660.7121.6380.102-0.2342.567lnGDPIC1.0260.06017.024< 0.00010.9071.144lnDist-0.8130.175-4.655< 0.0001-1.157-0.470The table above gives the model parameter.

In the table we clearly observe that two independent variables (lnGDPIC and lnDist ) are significant 5% significance level. The coefficient of the intercept is shown to be -2.887 meaning that holding all other factors constant we expect the value of the dependent variable to be -2.887. The coefficient of lnGDPQatar is 1.166 meaning that for any unit decrease/increase in lnGDPQatar, we expect the dependent variable (lnExport) to decrease/increase by a factor of 1.166. Also, the coefficient of lnGDPIC is 1.

026 meaning that for any unit decrease/increase in lnGDPIC, we expect the dependent variable (lnExport) to decrease/increase by a factor of 1.026. Finally coefficient of lnDist is -0.813 meaning that for any unit decrease in lnGDPQatar, the dependent variable (lnExport) increases by a factor of 0.813 and vice versa.Correlation matrix:VariableslnGDPQatarlnGDPIClnDistlnExportlnGDPQatar1.000-0.0230.0430.040lnGDPIC-0.0231.000-0.0100.644lnDist0.043-0.0101.000-0.180lnExport0.0400.644-0.1801.000In the correlation matrix, we observe there is hardly a correlation between the dependent variable and the independent variables.

For instance, the correlation coefficient between InGDPQatar and INGDPIC is -0.023 (close to zero). Similarly, the correlation coefficient between InGDPQatar and INGDist is 0.043 (close to zero). However, there is an average positive correlation (0.644) between InExport and InGDPIC.