Regression Analysis

Linear Regression is the process to develop an equation to express the linear ( straight line ) relationship between two variables. For example , incase there is a correlation between two variables amount of money spent on advertising by Apple Computers and number of Apple computers sold, we may want to ascertain an equation that will fit the trend in data for us to be able to predict sales for varying amounts of ad spend. Lets demonstrate this with an example:

The Edison Electric company is studying the relationship between kilowatt hours ( thousands ) used and the number of rooms in a private single-family residence. A random sample of 10 homes yielded the following:

Number of Rooms	Killowatt-Hours (000)
13	10
10	8
15	11
7	6
11	9
9	7
11	9
11	11
6	5
7	8

The Least Square Principle. Our judgment is removed by determining the regression line using a math method known as the least square principle. This method gives what is commonly called the best-fitting line. It minimizes the sum of squares of the vertical distances between the actual Y values and the predicted values of Y. General form of the regression equation is Y' = a + bX

where Y' is the predicted value of Y variable for a chosen X value.
a is the Y-intercept, it is the estimated value of Y when X = 0.
b is the slope of the line,
X is any value of the independent variable that is chosen,

The values a and b in the regression equation are usually referred to as the estimated regression coefficients and they are computed as follows:

Slope of Linear Equation of Regression