Assumptions of the regression model

Like any other theory, the linear regression analysis is also based on certain assumptions. Consider the population regression model

There are four assumptions made about this model.

Assumption1: The random error term has a mean equal to zero for each x.

In other words, among all households with the same income, some spend more than predicted food expenditure; others spend less than predicted food expenditure. Some of positive errors equal to the sum of negative errors so that the mean of errors for all households with the same income is zero.

Assumption2: The errors associated with different observations are independent. According to this assumption, the errors for any two households are independent. All households decide independently how much spend on food.

Assumption3: For any given x, the distribution of errors is normal. In other words, food expenditure for all households with the same income are normally distributed.

Assumption4: The distribution of population errors for each x has the same (constant) standard deviation, which is denoted by . This assumption indicates that the spread of points around the regression line is similar for all x values.

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