The Concept of Linear Regression - Essay Example

Linear RegressionGenerally, regression is defined as a measure of a relation between the mean values of a given variable with the corresponding values of other variables. It is an attempt to describe the movements in a variable with regards to movement in other variables. Linear regression is a form of regression which attempts to build a linear model between dependent and independent variables. It is represented by the equationIn a linear equation,generally represents the intercept of the equation whilerepresents the slope of the equation.

The equation also aims to capture the error random term through. Linear regression is represented through two forms; simple linear regression and multiple linear regression. A simple linear regression attempts to build a linear model between a single independent and single dependent variable. However, a multiple regression model comprises of a single independent variable with multiple independent variables. For instance, stock returns are dependent on interest rates, risk, dividend payout ratio and various other variables.

The most common example of simple linear regression is market index model. It assumes that the returns on stock are only dependent on market returns (Elton & Gruber, 2007). Observations of the market often reveal that as the market goes up, the stock also follows the same direction. This implies that stock returns are correlated with market returns thus we can relate it to the stock market index. An example of multiple regression is cited in the literature by Lusztig & Schwab (1970), where multiple regression analysis was used to estimate the insurance expenses (dependent variable), through commission, profit and contingencies and premium taxes (independent Variables).

Minimum least (sum of squares) method is used to estimate the model for regression equation. The values are chosen in such a way that the (vertical) distances from the data points to the fitted lines are minimized (so that the line fits the data as closely as possible). The figure below shows the best fitted line for a simple linear regression model. It is generally represented by the equationWidgeCorp can utilize the regression model to forecast its future demand but for this we need to know which of the variables will impact the demand for cold beverage sales Price of the goodPrice of substitutes (Non-alcoholic and alcoholic beverages)Consumer IncomeTaste patterns of consumer (Degree of Health Consciousness)For instance, there is a general perception that there are indications that "soda and sweetened drinks are the main source of calories in American Diet," therefore most of the nutritionists recommend that soft drinks can be detrimental to health if they are consumed excessively.

So a multiple regression model for WidgeCorp can be formed by using the following independent variables which will help them in forecasting the future salesReferencesElton, E. J. & Gruber, M. J., (2007), Modern Portfolio theory Analysis and Investment Analysis, Wiley & Sons: New YorkLusztig , P. & Schwab, B., (1970). A Note On The Application Of Multiple Regression Analysis To Expense Allocation In The Insurance Industry, Journal Of Risk And Insurance , Issue 37, Volume 3; Pp-485