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Homework Exercise #3 Economics 4340 Fall, 2007 Dr. W. Ken Farr Name______

The data below show sales (Si), measured in billions of dollars ($), and profits (Pi), measured in millions of dollars ($) for 35 discount and fashion retailing companies in the United States.

Answer each question given below on lined sheets of paper if handwritten or typed and provide all necessary printouts to support your answers. Be neat!!

1. Assume that the data can be described by a simple linear regression model of the form Pi = b1 + b2Si + ei and that all the CRLM assumptions hold (along with the normality assumption). Use the ordinary least squares (OLS) estimator to estimate b1 and b2. Print out the regression results.

2. Perform t-tests for the null hypotheses that b1 = 0 and b2 = 0 at the 5 percent level of significance to check for statistical significance of the parameter estimates. In each case state the null and alternative hypotheses and the criterion for acceptance or rejection of the null hypothesis. Show the calculations for the t-statistics.

3. Briefly explain the economic meaning of the coefficient b2.

4. Explain the meaning of the coefficient of determination (r2) or (R2) for these results.

5. Forecast profits (P) when sales (S) is $4.

6. Print a scatter diagram showing sales (Si) on the x-axis and profits (Pi) and forecasted profits (Phati) on the Y-axis. Observation Sales (Si) Profits (Pi) 1 25.811 1075.9 2 53.794 1445.8 3 16.103 802 4 4.788 321.1 5 4.648 346.9 6 9.526 515 7 7.554 398.1 8 13.644 410 9 8.82 329 10 2.759 112 11 2.671 114.9 12 3.049 148.1 13 1.587 97.6 14 5.269 122.5 15 2.313 130.3 16 2.149 86.8 17 2.651 74.9 18 3.254 31.1 19 1.258 32.3 20 1.651 72.3 21 2.492 51.4 22 1.074 61.2 23 0.384 33.3 24 1.627 31.9 25 0.809 36.4 26 1.23 31 27 0.458 40.1 28 0.346 26 29 0.545 29.1 30 0.479 22.2 31 2.18 31.5 32 3.307 72 33 8.504 226 34 3.788 159 35 10.542 882.9