Simple Linear Regression

Regression analysis is a very valuable tool for today's manager. Regression has been used to model such things as the relationship between level of education and income, the price of a house and the square footage, and the sales volume for a company relative to the dollars spent on advertising. When business are trying to decide which location is best for a new store or branch office, regression models are often used. Cost estimation models are often regression models. The applicability of regression analysis virtually limitless.
There are generally two purposes for regression analysis. The first is to understand the relationship between variables such as advertising expenditures and sales. The second purposes is to predict the value of one variable based on the value of the other.
The simple linear regression model will first be developed, and then a more complex multiple regression model will be used to incorporate even more variables into our model. In any regression model, the variable to be predicted is called the dependent variable or response variable. The value of this is said to be dependent upon the value of an independent variable, which is sometimes called an explanatory variable or a predictor variable.
In any regression model, there is an implicit assumption (which can be tested) that a relationship exist between the variables. There is also some random error that cannot be predicted. The underlying simple linear regression model is:
Y = b0 + b1X + error

where:
Y = dependent variable (response variable)
X = independent variable (predictor variable or explanatory variable)
bo = intercept (value of Y when X = 0)
b1 = slope of regression line
error = random error
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