We see that the Sales of Natural Gas is dependent on various factors such as price of natural gas, prices of alternative fuels, exchange rate prevailing, construction index of the downstream industry etc. Further sales also varies with month e.g. in festive seasons plant is shut down hence it affects sales of natural gas. To develop a regression model, we begin by including all the predictors which affect sales. Gradually we proceed to models by rejecting some predictors which affect other predictors more than they affect sales of natural gas (response variable). We finally reach to our final model which explains how sales will change as the predictors change. Further we made sure to remove multi-collinearity, if any, between the predictors.

> summary(model3)

Call:lm(formula = Overall.Industry.sales ~ Construction.GDP + Price.of.Light.Diesel.Oil +Exchange.rate.previous.month + Construction.Indices + factor(Problem.Month),data = ngd)

Residuals:Min 1Q Median 3Q Max-11.9978 -2.9562 -0.5018 3.3431 11.3658

Coefficients:Estimate Std. Error t value Pr(>|t|)(Intercept) 161.08248 24.71411 6.518 1.86e-06 ***Construction.GDP -0.03780 0.03152 -1.199 0.243780Price.of.Light.Diesel.Oil 1.60654 0.74033 2.170 0.041623 *Exchange.rate.previous.month 1.40146 0.56050 2.500 0.020761 *Construction.Indices -1.22654 0.26759 -4.584 0.000161 ***factor(Problem.Month)1 -10.65135 3.58344 -2.972 0.007266 **---Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 5.932 on 21 degrees of freedomMultiple R-squared: 0.7216, Adjusted R-squared: 0.6553F-statistic: 10.89 on 5 and 21 DF, p-value: 2.876e-05

> vif(model3)Construction.GDP Price.of.Light.Diesel.Oil Exchange.rate.previous.month3.253469 2.025532 3.843513Construction.Indices factor(Problem.Month)3.514225 1.243415

==================================================================================> summary(model2)

Call:lm(formula = Overall.Industry.sales ~ Price.of.Furnace.Oil +

Price.of.Light.Diesel.Oil + factor(Problem.Month) + Exchange.rate.previous.month +Construction.Indices + Construction.GDP, data = ngd)

Residuals:Min 1Q Median 3Q Max-7.3353 -3.4516 -0.4015 2.3067 10.7983

Coefficients:Estimate Std. Error t value Pr(>|t|)(Intercept) 171.80231 22.64591 7.586 2.62e-07 ***Price.of.Furnace.Oil -3.64848 1.49148 -2.446 0.02381 *Price.of.Light.Diesel.Oil 4.91633 1.50787 3.260 0.00392 **factor(Problem.Month)1 -9.08508 3.28451 -2.766 0.01192 *Exchange.rate.previous.month 2.05811 0.57093 3.605 0.00177 **Construction.Indices -2.08766 0.42637 -4.896 8.72e-05 ***Construction.GDP 0.02563 0.03841 0.667 0.51222---Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 5.333 on 20 degrees of freedomMultiple R-squared: 0.7857, Adjusted R-squared: 0.7215F-statistic: 12.22 on 6 and 20 DF, p-value: 8.731e-06

> vif(model2)Price.of.Furnace.Oil Price.of.Light.Diesel.Oil factor(Problem.Month)12.073895 10.396771 1.292534Exchange.rate.previous.month Construction.Indices Construction.GDP4.934316 11.039211 5.977956

================================================================================== summary(model1)

Call:lm(formula = Overall.Industry.sales ~ ., data = ngd)

Residuals:Min 1Q Median 3Q Max-6.5670 -2.9980 0.0701 3.3486 7.8138

Coefficients:Estimate Std. Error t value Pr(>|t|)(Intercept) 85.88113 39.66632 2.165 0.043317 *Price.of.Furnace.Oil -2.07046 1.46673 -1.412 0.174229Price.of.Light.Diesel.Oil 3.16451 1.51053 2.095 0.049808 *Price.of.Natural.gas -2.50096 0.99491 -2.514 0.021119 *Exchange.rate.previous.month 3.52109 0.77214 4.560 0.000214 ***Problem.Month1 -9.49978 2.92385 -3.249 0.004223 **Construction.GDP 0.02463 0.03414 0.721 0.479491Construction.Indices -1.35795 0.47735 -2.845 0.010361 *---Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 4.74 on 19 degrees of freedomMultiple R-squared: 0.8392, Adjusted R-squared: 0.78F-statistic: 14.17 on 7 and 19 DF, p-value: 2.474e-06

vif(model1)Price.of.Furnace.Oil Price.of.Light.Diesel.Oil Price.of.Natural.gas14.781633 13.208208 21.217310Exchange.rate.previous.month Problem.Month Construction.GDP11.425433 1.296662 5.978775Construction.Indices17.517264

cor(xymat) Overall.Industry.sales Price.of.Natural.gas Price.of.Furnace.OilOverall.Industry.sales 1.00000000 -0.3222288 0.2722546Price.of.Natural.gas -0.32222882 1.0000000 0.5476639Price.of.Furnace.Oil 0.27225457 0.5476639 1.0000000Price.of.Light.Diesel.Oil 0.15615765 0.6407794 0.8626762Exchange.rate.previous.month -0.07713708 0.9409466 0.6371646Problem.Month -0.30145718 -0.1046645 -0.1195980Construction.GDP -0.29426622 0.8162618 0.5040496Construction.Indices -0.51053881 0.8772510 0.2816683 Price.of.Light.Diesel.Oil Exchange.rate.previous.month Problem.MonthOverall.Industry.sales 0.15615765 -0.07713708 -0.30145718Price.of.Natural.gas 0.64077940 0.94094662 -0.10466449Price.of.Furnace.Oil 0.86267622 0.63716458 -0.11959802Price.of.Light.Diesel.Oil 1.00000000 0.72295682 -0.08775713Exchange.rate.previous.month 0.72295682 1.00000000 -0.07508164Problem.Month -0.08775713 -0.07508164 1.00000000Construction.GDP 0.51504544 0.72749111 -0.29852129Construction.Indices 0.54346872 0.78438751 -0.07044044 Construction.GDP Construction.IndicesOverall.Industry.sales -0.2942662 -0.51053881Price.of.Natural.gas 0.8162618 0.87725095Price.of.Furnace.Oil 0.5040496 0.28166830Price.of.Light.Diesel.Oil 0.5150454 0.54346872Exchange.rate.previous.month 0.7274911 0.78438751Problem.Month -0.2985213 -0.07044044Construction.GDP 1.0000000 0.78258416Construction.Indices 0.7825842 1.00000000