Vehicle Sales Forecasting Using Regression

library(stats)
library(readxl)
veh <- read_excel("D:/PG Business Analytics/AS/Regression/data_test.xlsx")

head(veh)

Now, performing Setpwise Linear Regression to get best fit

step(lm(Sales ~ PassengerCars+OECD+PMI+Confidence+PLR+IIP_perc+IIP+Mahindra_sales+GDP_Agri+GDP_Total+Production+SCO_Prodn+MCY_Prodn+MPD_Prodn+JanD+FebD+MarD+AprD+MayD+JunD+JulD+AugD+SepD+OctD+NovD+Petrol_Delhi_prices+Time_Dummy+Dummy2008, 
                   data = veh))

Using the output to perform Regression

fit<-lm(Sales ~OECD + PMI + PLR + IIP_perc + Production + JanD + FebD + 
            MarD + AprD + MayD + JunD + JulD + SepD + OctD + NovD + Petrol_Delhi_prices + 
            Time_Dummy,data = veh)
summary(fit)

Call:
lm(formula = Sales ~ OECD + PMI + PLR + IIP_perc + Production + 
    JanD + FebD + MarD + AprD + MayD + JunD + JulD + SepD + OctD + 
    NovD + Petrol_Delhi_prices + Time_Dummy, data = veh)

Residuals:
   Min     1Q Median     3Q    Max 
-66348 -13968   2496  13331  66470 

Coefficients:
                      Estimate Std. Error t value Pr(>|t|)    
(Intercept)         -5.825e+05  3.626e+05  -1.606 0.111794    
OECD                 8.724e+03  4.596e+03   1.898 0.061002 .  
PMI                  5.708e+02  2.500e+02   2.284 0.024831 *  
PLR                 -1.049e+04  5.196e+03  -2.018 0.046662 *  
IIP_perc            -2.003e+03  8.796e+02  -2.278 0.025200 *  
Production           8.629e-01  4.392e-02  19.648  < 2e-16 ***
JanD                 2.157e+04  1.134e+04   1.902 0.060464 .  
FebD                 2.182e+04  1.114e+04   1.959 0.053349 .  
MarD                 4.076e+04  1.120e+04   3.640 0.000462 ***
AprD                 3.499e+04  1.121e+04   3.121 0.002444 ** 
MayD                 3.112e+04  1.131e+04   2.751 0.007237 ** 
JunD                 1.917e+04  1.114e+04   1.720 0.089020 .  
JulD                -3.479e+04  1.122e+04  -3.100 0.002604 ** 
SepD                 3.951e+04  1.197e+04   3.302 0.001394 ** 
OctD                 5.263e+04  1.236e+04   4.257 5.21e-05 ***
NovD                 2.321e+04  1.160e+04   2.001 0.048471 *  
Petrol_Delhi_prices  1.833e+03  9.159e+02   2.001 0.048507 *  
Time_Dummy          -6.251e+03  3.035e+03  -2.060 0.042432 *  
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 26870 on 87 degrees of freedom
Multiple R-squared:  0.9927,    Adjusted R-squared:  0.9912 
F-statistic:   693 on 17 and 87 DF,  p-value: < 2.2e-16

The Best fit output gives an R-square of 0.9927 and Adjusted R-Square of 0.9912. The P-value of 2.2e-16.

Interestingly the sales take a dip in July and are maxinum in the month of October. This can be further explained by seasonality Index.

Also petrol prices have a significant impact on Sales.