## Multiple linear regression models, Mathematics

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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 + b1x1 +b2x2 +............ + bnxn

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.

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