Its name tells us the criterion used to select the best fitting line, namely that the sum of the squares of the residuals should be least. In other words, the least squares regression equation is the line for which the sum of squared residuals is a minimum (Dallal, 2008).
Multiple regression – the general purpose of multiple is to learn more about the relationship between several independent variables and a dependent variable. For example, a real estate agent might record for each listing the size of the house in square feet, the number of bedrooms, the average income in the respective neighborhood, and a subjective rating of appeal of the house. As soon as this information is compiled for different houses it would be exciting to see whether these measures relate to the price for which a house is sold.
One good example for a simple linear regression analysis can be found in the financial industry, specifically in the stock market.
Lets assume that a stock broker would like to estimate the tradeoff between risk and returns he/she would use linear regression to estimate the returns compared to the risk. If the risk increases the return will increase and vice versa. The stock price of a company would be the dependent variable, while the market or index for the industry would be the independent variable. Now if the correlation coefficient between those variable is 2.2 then an increase in the market by 1% would increase the stock price by 2.2%. The same holds true if the market goes down or decreases.
Another good example for multiple linear regression analysis can be seen in biochemistry and drug industry. The application.