Regression Assumptions

Assumptions

In linear regression analysis it is assumed that the relationship between y and x can be expressed in the form

y = ( a + b x ) + e

where e represents the unpredictable element in y due to random variation or measurement error. This random element explains why different values of y are obtained for the same value of x. Without this random element there would be no need for regression analysis since the value of y would be perfectly predictable from the value of x. Because of the random element you can only estimate the values of a and b by the intercept a and slope b of the line of best fit. Hence any predictions you make based on the line are also only estimates. To be able to quantify the reliability of these estimates you must make the following assumptions:

	the assumption of linearity
	the assumption of independence
	the assumption of constant variance
	the assumption of Normality

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