## Eliminate all of the insignificant variables, Applied Statistics

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The file Midterm Data.xls has a tab labeled "Many vs. S&P" which presents historical price data for several assets, a volatility condition (VIDX = 1 if the NYSE volatility is greater than 0.04), Schlumberger, Westinghouse Air Brake, Ford and Eastman Kodak. Create a multiple regression model of the S&P 500 using the other asset prices as the independent (x) variables.

Answer the following questions based on the Excel output report. Support your answers with numbers from the output report. Use level of significance = 0.05.

• Write the estimated multiple regression equation. Note: Use actual variable names and numbers. If using symbols, define them before using in the equation.

• Clearly explain the meaning of b1 (the coefficient of Schlumberger). Note: Use actual variable names and numbers in answering your question. b1 is the slope is not a sufficient answer.

• Clearly explain the meaning of b2 (the coefficient of Westinghouse Air Brake). Note: Use actual variable names and numbers in answering your question. b2 is the slope is not a sufficient answer.

• Clearly explain the meaning of b3 (the coefficient of Ford). Note: Use actual variable names and numbers in answering your question. b3 is the slope is not a sufficient answer.

• Clearly explain the meaning of b4 (the coefficient of Eastman Kodak). Note: Use actual variable names and numbers in answering your question. b4 is the slope is not a sufficient answer.

• Clearly explain the meaning of b5 (the coefficient of Volatility). Note: Use actual variable names and numbers in answering your question. b5 is the slope is not a sufficient answer.

• Is the regression equation significant? Give reasons for your answer. (Hint: The answer to this question requires test of the hypothesis: Ho: 1 = 2 = 3 = 4 = 5 = 0 vs. Ha: At least one j is not equal to zero, where j = 1...5)

• Which variables in the current equation are significant and which are not significant? Give reason for your answer. (Hint: The answer to this question requires test of hypothesis: Ho: j = 0 vs. Ha: j 0 for j = 1...5).

• Eliminate all of the insignificant variables and show the final regression equation.

• Considering the original regression equation from a), if you already have an S&P 500 fund in your portfolio, what is the best new asset to place in the portfolio? (Remember, you want your portfolio to be as diverse as possible.) Are there any possible practical limitations to using some of these stocks in a portfolio.

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