# Econometrics Paper

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Econometrics Paper

Minimize  = ….we’ll come back to this later

For now, however, we can manually compute the residuals by hand.  Fill in the table.

 i 70 95 65 100 90 120 85 140 110 160 115 194 120 265 148 220 155 236 150 260 verify this sum = 0

The symbolshould have a subscript i to indicate it is not a constant, however, the equation editor does not depict this in a visually appealing manner.

Problem Set A (Fall 2016) You may work with anyone (fellow classmates, not an outside professional) but hand in your own paper. Hand in one, single document (please use the abbreviated answer sheet provided) that is stapled or bounded together in a very, professional manner. _____________________________________________________________ 1. Presented below are hypothetical data on weekly family consumption expenditure Y and weekly family income X. A. Obtain the sample regression function (with computed values) for this data using SAS (write the program in the SAS editor using a cards statement as we did in class). Provide the following: Using symbols, what does the population regression function (PRF) look like (refer to the text if needed)? _____________________________________________________________ Using symbols, what does the sample regression function (SRF) look like? _____________________________________________________________ Based on your SAS output, what is the SRF with the estimated values? ____________________________________________________________ B.

Obtain a correlation matrix for this data. What is the coefficient of correlation indicating about the direction and strength of the 2 variables? C. Now we will produce the sample regression estimates by hand. Compute the sample intercept b1 and sample slope b2 manually. Remind me to give you the formulas in lecture. To help, use the columns set up below to start: yi xi 70 95 65 100 90 120 85 140 110 160 115 194 120 265 148 220 155 236 150 260 D.

We discussed in class the nature of the residuals, ei . When we do Ordinary Least Squares regression (OLS), we choose b1 and b2 in such a way that the residuals are as small as possible1 . The way we do this is to make the residual sum of squares (RSS), ei 2 , as small as possible. In other words, we have a minimization problem!