Multiple Linear Regression Models
There are situations whether there is more than one factor which influence the dependent variable
Illustration
Cost of production weekly in a large department depends on some factors:
i. Total numbers of hours worked
ii. Raw material utilized during the week
iii. Total number of items produced during the week
iv. Number of hours spent on maintenance and repair
This is sensible to use all the identified factors to predict department costs. Scatter diagram will not provide the relationship between total costs and the various factors. The linear model for multiple linear regressions if of the type that is the line of best fit
y = α + b_{1}x_{1} +b_{2}x_{2} +............ + b_{n}x_{n}
We suppose that residuals or errors are negligible. In order to choose among the models we examine the values of the multiple correlation coefficient r and the standard deviation of the residuals α. A model that describes well the relationship between x and y's has multiple correlation coefficient r close to ±1 and the value of α which is small.