rcept and deterministic trend (Gujarati & Porter, 2009). However, still the null hypothesis is not rejected and the FDI inflows are non-stationary. Thus, the first-order differentiation for the variable was done. DifflnFDI series is generated which represents the stationary form of FDI inflows.
In the case of DifflnFDI, stationarity is derived as the absolute value of test statistic is greater than critical value and the p-value is also small i.e. 3.584 > 3.000 and 0.0061 < 0.05. Thus, DifflnFDI is a stationary variable.
Cointegration test studies the nature of the relationship between the variables. It determines whether there is any relationship or linkage between the variables or not. The existence of cointegration between the variables ensures that there is a linkage between the variables and no spurious or non-sense relationship is studied (Gujarati & Porter, 2009). Johansen’s cointegration results for testing the long-run relationship between FDI inflows and water temperature of Indian rivers are given below.
|Max. Ranks||Trace Statistic||5% Critical Value||Max Statistic||5% Critical Value|
*represent significant at 5%level
The null hypothesis of no cointegration is rejected for 0 ranks as the values are greater than critical value i.e. 20.3730 > 15.41, and 17.6082 > 14.07. Furthermore, for 1 rank the null hypothesis is not rejected i.e. 2.7649 < 3.76.
Hence, at most 1 cointegrating vector exists between FDI inflows and water temperature Kumar & Chander, (2016). Thus, the results of trace statistic and max statistic shown in Table 2 depicts that long-run and short-run relationship exists between FDI inflows and water temperature.
A dataset is said to be normally distributed if the values are symmetrically distributed. The existence of normality in the value of the variables is the assumption of the classical linear regression (Casson & Farmer, 2014). Thus, to depict the impact of FDI inflows on water temperature, the normality of the data is tested. Shapiro-Wilk test was used and the result of the test is represented below.
The p-value for lntemp and Difflnfdi is greater than the significance level of the study i.e. 0.21856 and 0.50621 > 0.05. Therefore, the null hypothesis of the normal distribution is not rejected and both variables are normally distributed. Hence, the regression test can be performed.
Step 2: Regression
The stationary, cointegrated, and normally distributed variables were used to form the regression model.
|Variables||Nature of variable||Description|
|Dependent||Stationary form of Natural Log-transformation for average water temperature of Indian rivers at the t-time period|
|Independent||Stationary form of Natural log-transformation for net FDI Inflows at the t-time period|
|Coefficients||Intercept, Slope Coefficient|
The results for the regression of the above model is shown below
|LnTemp||Coefficient||t-value||p-value||R2 value||Adjusted R2 value|
The results of the regression model show an R2 value of 0.3272 and an adjusted R2 value of 0.2755. However, it is important to test the heteroscedasticity and autocorrelation presence in the model (Casson & Farmer, 2014) to derive unbiased and efficient results.
Step 3: Diagnostic tests
Autocorrelation means the existence of interdependence between the error terms. The presence of autocorrelation in the model lead to decreasing the validity and precision of the results of the model. No autocorrelation is also the assumption of classical linear regression (Huitema & Laraway, 2006). Durbin Watson test determines whether the residuals are interrelated. The result is presented below.
The Durbin Watson test for the above model has shown the following result.
As the D-statistic is between DU and 4-DU i.e. 1.543<2.147329<2.457, thus there is no autocorrelation present in the model. Okumoko, Akarara, & Opuofoni, (2018) stated that the value of the Durbin Watson statistic should be close to 2 to derive reliable results. As the value of D-statistic is close to 2, thus, the residuals are not related to each other, which makes the results of the regression reli