Problem: Suppose your employer buys you a copy of Excel and you decide to learn regression analysis. You gather some historical data on Sales and Advertising expenses and run a simple regression using Sales as the dependent variable and Advertising Expense as the independent variable. The results you get are shown below, with the relevant items I want you to focus on in boldface. After pondering the results a while, you show the data to your boss and she asks the questions listed below the table. Answer the questions, keeping in mind that you are explaining your answers to a supervisor who is not conversant with economic theory.
Note: The key to this question is that you are being asked to provide statistical answers, but phrasing the explanations for the statistics in a fashion that a non-statistical person can understand (a very real and common situation).
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Regression Statistics
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Multiple R
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0.834
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R Square
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0.747
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Adjusted R Square
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0.75
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Standard Error
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317.105
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Significance F
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.00001
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Coefficients
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Standard Error
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t Stat
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P-value
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Lower 95%
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Intercept
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10,000.0
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81.72330008
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0.551528
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0.588449
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-127.3486476
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X Variable 1
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-5.5
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0.153318278
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8.4
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9.61E-06
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0.627810145
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Q1. How do I convert the above information to an equation I can use? Write out that equation using the numbers provided and the following information:
Sales (S) is the dependent variable
Advertising Expense (A) is the independent variable
Q2. Someone who knows statistics told me that the t value (labeled t stat in boldface above) refers to the significance of the X variable. They used a table to tell me the t value of 8.4 indicates that the X variable is statistically significant at the .05 level. What does that mean in practical terms?
Q3. What would this firm’s sales be if it didn’t advertise? How does one interpret that number, that is, what does it represent?
Q4. There is something basically wrong with the regression equation (the answer to part a), i.e. the equation describes a relationship that probably isn’t correct. Explain what is wrong and why?