Linear regression involves an approach used to model the link between a dependent scalar variable (Y) and an explanatory variable (X). Whenever one explanatory variable is used, the case is known as a linear simple regression. In cases where more than one variable is used, the case is known as linear multiple regression. For the linear regression, the modelling of the data occurs using a linear function predictors together with the parameter models that are not known thus estimated from the given data. A model of this kind is known as a linear model. In many situations, linear regression involves a model such that the conditional mean for the Y provided the X value is an X affine function. This means that linear regression is vital in modelling the link between variables through fitting a linear equation of the given data. In many cases, explanatory variable forms one of the variables in a linear regression where as the dependent variable forms another variable. In attempts to understand the linear models, this paper explores linear regression using six data points.
Table 1 shows out a set of six data points obtained from the data of US Yellow Corn Kcty and US Yellow Corn Mpls in U$/BSH.
Table 1
|
US Yellow Corn Kcty in U$/BSH |
|
|
6.42 |
5.84 |
|
6.61 |
6.03 |
|
6.59 |
6.07 |
|
6.65 |
6.13 |
|
6.82 |
6.3 |
|
6.83 |
6.31 |
|
7.04 |
6.52 |
From table 1, graph was plotted to display the scatter plots and the regression function.
Graph1: US Yellow Corn Mpls in U$/BSH versus US Yellow Corn Kcty in U$/BSH.
The regression equation is given as;
US Yellow Corn Mpls in U$/BSH= -1.1668 + 1x US Yellow Corn Kcty in U$/BSH.
From the linear regression analysis, it is vivid that in the US Yellow Corn Mpls in U$/BSH, a = 1, b = -1.1668, R2 = 0.990094, r (coefficient of correlation)= 0.995035. It is prudent to say that US Yellow Corn Mpls in U$/BSH and Yellow Corn Kcty in U$/BSH are positively correlated. This means that, in the US Yellow Corn Mpls in U$/BSH and Yellow Corn Kcty in U$/BSH the level of flexibility and strength increases. The level of association in the two variables is extremely stringer in the US Yellow Corn Mpls. This also means that the production of US Yellow Corn Mpls increases with the production of Yellow Corn Kcty.
This model shows out the relationship between a response variable (US Yellow Corn Mpls in U$/BSH) and a unit predictor variable (Yellow Corn Kcty in U$/BSH), whenever the other predicting variables are held fixed. This information is extremely vital to not only a businessperson but also consumers. In this respect, whenever the market experiences an increase in the US Yellow Corn Mpls production and supply, it means that both consumers and business people need to be ready for an increase in the production and the supply of Yellow Corn Kcty. For this reasons, both consumers and the traders would be able to save enough money for the purchase of these products. On the other hand, whenever there is a shortage in the production and the supply of US Yellow Corn Mpls in the market, the consumers and traders would be able to prepare for a relative shortage in the production and supply of Yellow Corn Kcty in U$/BSH. In this case, both the traders and consumers would be able to make enough purchases that will take care of the expected future shortage.
