Statistical analysis and forecast of consumption of lube oil in India.

Multiple regression is the study of how a dependent variable y is related to two or more independent variables. In other way, Multiple Regression is a statistical method for estimating the relationship between a dependent variable and two or more independent (or predictor) variables. Simply, MLR is a method for studying the relationship between a dependent variable and two or more independent variables.

Multiple Regression EquationE(Y) = B0 + B1X1 + B2X2 + B2X2 + B3X3 +..+ BpXp +

In the Multiple regression equation, B0 , B1 , B2 , B3 ,.., Bp are the parameters and the error term Is the random variable. The least square method is used to develop the estimated regression equation for the best approximated straight line relationship between the dependent and independent variables.

In our case, we have taken the data for ten years from 2004-05 to 2013-14. Here, we have taken four independent variables and one dependent variable. The four dependent variables are number of vehicles, Personal disposable income, populations and crude oil price, whereas the independent variable is consumption of lube oil annually. The most widely used SPSS Statistics is used for statistical analysis. The output of SPSS after performing multiple regression are as follows:

Table: Mean and standard deviation for all the variables.

The data Descriptive Statistics shows the mean and standard deviation of consumption of lube oil, Number of vehicles, Personal Disposable Income, Populations and the crude oil prices. In our analysis, we have taken data of 10 years or 120 months.

Table: Correlation values among all the variables.

Correlation table shows the Pearson correlation coefficient to show the correlation between the of consumption of lube oil, Number of vehicles, Personal Disposable Income, Populations and the crude oil prices. The maximum correlation with consumption of lube oil (dependent variable) is found between the population and number of vehicles around 0.857 correlation is very strong positive correlation. It means the consumption of lube oil will grow with the population and number of vehicles. As population and number of vehicles will increase the consumption of lube oil, in the future, will increase.

Table: Coefficients in tabular form to get the multiple regression equation

The coefficient table shows the value of beta which is the correlation between consumption and independent variables. Here the significance of this correlation is determined by t distribution. The value of the significance ranges from 0.143 to 0.929 where which means correlation is significant. The other term Unstandarized Coefficients explains that what will be the consumption of lube oil if we increase the respective independent variable by 1. Using above table we arrive to following multiple regression equation which is as follows:

Y = -16228.15 +4.13E-05 A + -0.028 B + 16.603 C + 0.88 DWhere,A = Number of vehiclesB = Personal Disposable IncomeC = PopulationD = Crude oil priceY = Consumption of lube oil