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Write a 6 page essay on Data Anlaysis.Use a calculator and your sample to calculate ∑X, ∑Y, ∑XY and ∑X2. Use these values to write down the pair of ‘normal equations’ the solutions of whic
Write a 6 page essay on Data Anlaysis.
Use a calculator and your sample to calculate ∑X, ∑Y, ∑XY and ∑X2. Use these values to write down the pair of ‘normal equations’ the solutions of which give the constant term (a) and the slope coefficient (b) of the fitted Ordinary Least Squares line Y = a + bX.
Step 2.This step involves taking the partial derivatives and setting them equal zero provides us with candidate points for a minimization or maximization. In this step we write the equation that the partial derivatives will be taken in matrix form.
Step 3.The partial derivatives of the matrix is taken in this step and set equal to zero. b is a vector or coefficients or parameters. Because the equation is in matrix form, there are k partial derivatives (one for each parameter in b) set equal to zero.
Step 4.Simple matrix algebra is used to rearrange the equation. The first order conditions are to set the partials equal to zero. First, all terms are divided by the scalar 2. This removes the scalar from the equation. This is simply for ease. Second, is added to both side of the equation. On the left hand side, the two terms and cancel each other out leaving the null matrix. This step moves to the right hand side.
Step 5.Finally, b is found by pre multiplying both sides by . Division by matrices is not defined, but multiplying by the inverse is a similar operation. Recall, , where I is the identity matrix. Multiplying any matrix, A, by I results in A, similar to multiplying by one in linear algebra.
The coefficient of GDP is 0.0098662. So for every unit increase in .GDP, a .0.0098662 unit increase in .IN .is predicted, holding all other variables constant. On the other hand the p-value associated with the GDP is 0.800 a value greater than 0.05 (significance level), we thus fail to reject the null hypothesis and conclude that the coefficient for .GDP .(.0098662) is not statistically significantly different from 0. Thus at 5% level of significance
