# Regression Analysis of VST Tractors and Tillers Ltd.

### INTRODUCTION

VST group started in 1920 dealing in petroleum products. In 1965, the group promoted M/s VST tillers and Tractors Ltd. in collaboration with Mitsubishi Group, Japan. It is engaged in production of power tillers, tractors and diesel engines. It is marketing its product in regions of Asia, Middle East, Africa, Europe and USA.

### VST Tillers

VST Tillers is the first company to introduce higher horsepower direct injection technology in India. The company has 3 types of power tillers in its product range, that is, VST SHAKTI 130DI, VWH120 and AD8V. With the help of its long association with Mistubishi Group, the company has got the latest technology which has helped it to meet the exacting requirements of customers.

### REGRESSION ANALYSIS

">

### Theory

Regression analysis is basically carried out to determine the value of parameters of a function that cause the function to best fit a set of data observations.

The regression line is the line obtained by minimising the sum of the squared vertical deviations of each point from the regression line.

In our case, the function relates the effect of price of tillers, price of a substitute of tillers (Tractors) and income of people on the demand of Tractors. Hence, we can write the function as follows:

Q = f (P, Pt, I)

Where,

Q = Sale of Power Tillers

P = Price of Power Tillers

Pt = Price of tractors

I = Income

This can be shown as,

Q = k + a*P + b*Pt + c*I

Where k, a, b and c are the parameters which we will find through the regression analysis. The value of a, b and c will give an indication as to how the consumption changes when any of the independent variables, that is, price of tillers, price of tractors or income changes.

### Statistics from Regression Analysis

Apart from the values of k, a, b, c and c regression analysis gives us a lot of other parameters:

t statistic or t ratio: The higher the value of the calculated t ratio, the more confident we are that the true but unknown values of the parameters that we are seeking is not equal to zero (i.e. that there is a significant relationship between advertising and sales). The value of t statistic is a indicator of significance of parameters.

R2: This is known as coefficient of determination. It measures the proportion of the explained to the total variation in the dependent variable in the regression analysis. This parameter gives the fit.

Adjusted R2: When the dependent variable that we seek to explain is hypothesized to depend on more than one independent variable, we have multiple regression analysis. In order to take into consideration the reduction in the degrees of freedom as additional independent variables are included in regression, we calculate adjusted R2.

F Statistic: The F statistic can test the null hypothesis that no connection exists between the dependent variable and all or some of the independent variables.

### Data and Analysis

For our purpose of regression analysis, we will use the following data

Year |
Annual sale of VST tillers |
Price of tractors |
Price of Power tillers |
GDP/ person |

1997 |
57379 |
203232 |
68745 |
425.759 |

1998 |
67780 |
215889 |
73071 |
429.253 |

1999 |
69396 |
224060 |
75402 |
434.182 |

2000 |
70571 |
231234 |
75681 |
439.617 |

2001 |
79237 |
240335 |
79925 |
442.68 |

2002 |
57684 |
252902 |
81105 |
455.68 |

2003 |
44862 |
254799 |
83570 |
519.22 |

2004 |
46984 |
267165 |
86478 |
596.97 |

2005 |
62727 |
286066 |
91148 |
688.7 |

2006 |
81556 |
296118 |
93710 |
756.67 |

2007 |
99797 |
309929 |
94900 |
939.52 |

2008 |
95370 |
328610 |
96723 |
1016.16 |

TABLE1:Data for regression analysis (1997-2008)

### Analysis

Following is the detailed analysis of the regression test on the given data.

Dependent Variable: Q | ||||

Method: Least Squares | ||||

Date: 08/16/09 Time: 13:45 | ||||

Sample: 1997 2008 | ||||

Included observations: 12 | ||||

Variable |
Coefficient |
Std. Error |
t-Statistic |
Prob. |

C |
7512.193 |
3406.765 |
2.205081 |
0.0585 |

PT |
0.017443 |
0.011278 |
1.546684 |
0.1605 |

P |
-0.131622 |
0.060277 |
-2.183630 |
0.0605 |

I |
10.97785 |
2.793648 |
3.929576 |
0.0044 |

R-squared |
0.911261 |
Mean dependent var |
7545.250 | |

Adjusted R-squared |
0.877983 |
S.D. dependent var |
2065.657 | |

S.E. of regression |
721.5526 |
Akaike info criterion |
16.26189 | |

Sum squared resid |
4165106. |
Schwarz criterion |
16.42352 | |

Log likelihood |
-93.57134 |
F-statistic |
27.38385 | |

Durbin-Watson stat |
1.829769 |
Prob(F-statistic) |
0.000147 | |

Estimation Equation:

=====================

DEMAND = C(1) + C(2)*PRICE + C(3)*PRICE OF TRACTOR + C(4)*INCOME

Substituted Coefficients:

=====================

DEMAND = 7512.193 - 0.131622 *PRICE + 0.017443*PRICE OF TRACTOR + 10.97785*INCOME

Coefficients: As can be seen from the above equation, the coefficients of price of tillers and tractors are (-0.131622) and (0. 017443) respectively and that of income is (10.97785). This implies that the demand for tractors decreases by 0.131622 units for every increase by one Rupee in price. It also increases by 0.017443 units for rupee increase in price of tractors and increases by 10.97785 per increase in income.

Std. Error: The standard error of each parameter tells how certain we can be of the best fit value. In the above model the standard error of all factors is relatively small. This means that we can be confident about the relevance of these factors.

t-statistic: The t-statistic is a measure of how relevant the factor is to the regression. It should be above 2.306 for a 5% confidence that the factor is relevant to the regression. In the above model the t-statistic for income is comfortably over the threshold implying that it is an important factor in determining the demand. The price factors are more border line with t-stat for price of tractors being a lower than threshold value. This means that the factor is not very relevant to the demand estimate.

R-square: The R-square value for the model is 0. 911261. This is a measure of goodness of fit of the regression curve to the actual function governing the demand. According to the R-square statistic, 91% of the behavior is explained. This however is not a true estimate as R-square stat tends to overestimate fit in case of more than one variable.

Adjusted R2: The value of adjusted R2 is 0. 877983. This is a better measure of goodness of fit than R-square metric. This value implies that our model explains close to 88% of the demand when the effect due to multiple variables is accounted for.

F Statistic: The value of F stats in the model is 27.38385. This is high enough for us to refute the null hypothesis and thus accept the alternate. I.e. there is a significant relation between the dependent and the independent variables.

Standard Error of Regression: This value for the above model is close to 721.5526. This can be considered relatively mid-level value signifying good fit of regression.

### Interpretation

From the above model we can infer that, in case of VST tillers, the demand is affected by price of the tractor, price of tillers and income. We can see from the above model that the demand for tillers is adversely affected by increase in their price and increases with increase in price of tractors. Also with increase in income the demand for tillers also increases.

### Conclusion

We started by assuming that the demand for VST tillers depends on its price, the price of a substitute (tractors) and income of the consumers. We then tried to find relationship between the independent variables and the dependent variable. For this we used regression (Least Square method) and we saw that-

- The demand increases with increase in income.
- The demand is affected by movement in price of tillers and tractors.