Islamic finance uses regression analysis. Often a relationship is found to exist between two (or more variables). For example, there is a close relationship between investment in human capital and economic growth, and between education and income. Similarly, there is a relationship between price and demand or price and supply of a product; for instance, the high price of oranges may reduce consumption of oranges. Similarly, the high price of oranges may increase the supply of oranges. In Islamic, finance, there is a relationship between the returns of a security and the market portfolio return, called the *capital asset pricing model* (CAPM). Many other relationships exist between financial variables.

It is frequently desirable to postulate an equation that connects the variables and then use data to estimate the parameters of the equation.^{1} In this chapter we explore techniques for estimating linear regression based on empirical data. The method of estimation is called the *ordinary least squares* method (OLS). It is the most used method in many fields of science. We present the principle of estimation based on choosing parameters of the model that minimize the sum of squared errors (SSE) between actual data and fitted data. We present the techniques for deriving the estimated parameters, the probability distributions and significance tests of these parameters, and we discuss the goodness of fit of the regression. We show how a regression is used to ...

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