Linear regression
- Thread starter liordp
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Hi Convexity,
The reference is Gujarati 6.6. Here is similar para from Gujarati:
"The second interpretation of linearity is that the conditional expectation of Y, E(Y | Xi ), is a linear function of the parameters, the ß’s; it may or may not be linear in the variable X. In this interpretation E(Y | Xi ) = ß1 + ß2 * X^2 is a linear (in the parameter) regression model. To see this, let us suppose X takes the value 3. Therefore, E(Y | X = 3) = ß1 + 9*ß2 , which is obviously linear in ß1 and ß2. Now consider the model E(Y | Xi ) = ß1 + ß2^2 * Xi . Now suppose X = 3; then we obtain E(Y | Xi ) = ß1 + 3*ß2^2, which is nonlinear in the parameter ß2. The preceding model is an example of a nonlinear (in the parameter) regression model...
Of the two interpretations of linearity, linearity in the parameters is relevant for the development of the regression theory to be presented shortly.Therefore, from now on the term “linear” regression will always mean a regression that is linear in the parameters; the ß’s (that is, the parameters are raised to the first power only). It may or may not be linear in the explanatory variables, the X’s. "
David
The reference is Gujarati 6.6. Here is similar para from Gujarati:
"The second interpretation of linearity is that the conditional expectation of Y, E(Y | Xi ), is a linear function of the parameters, the ß’s; it may or may not be linear in the variable X. In this interpretation E(Y | Xi ) = ß1 + ß2 * X^2 is a linear (in the parameter) regression model. To see this, let us suppose X takes the value 3. Therefore, E(Y | X = 3) = ß1 + 9*ß2 , which is obviously linear in ß1 and ß2. Now consider the model E(Y | Xi ) = ß1 + ß2^2 * Xi . Now suppose X = 3; then we obtain E(Y | Xi ) = ß1 + 3*ß2^2, which is nonlinear in the parameter ß2. The preceding model is an example of a nonlinear (in the parameter) regression model...
Of the two interpretations of linearity, linearity in the parameters is relevant for the development of the regression theory to be presented shortly.Therefore, from now on the term “linear” regression will always mean a regression that is linear in the parameters; the ß’s (that is, the parameters are raised to the first power only). It may or may not be linear in the explanatory variables, the X’s. "
David
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