ECON 483: Forecasting

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Empirical homework 1

The data for the homework assignment is available in EasyReg space delimited text format (*) and as an Excel CSV file (**). These data files contain information on the percentage change in total sales (= X) and profits (= Y) of 26 stores of a retail chain (think of Lowes or Walmart) in different cities in a particular year. The cities are far enough apart to assume that the 26 observations involved are independent.

1. Import the data in EasyReg or any other econometrics software package. Select the variable Y (= %change in profits) as the dependent variable and the variable X (= %change in total sales) as the explanatory variable. Estimate the regression model

   Y_j = a + bX_j + U_j

   by ordinary least squares (OLS), using all available data. (j = 1,...,26). Present the results.

2. You may assume that the model errors U_j are normally N[0,s²] distributed. Given this assumption and the estimation results, test at the 5% significance level the hypotheses:
   • b = 0 against b ¹ 0.
   • b = 0 against b > 0.
   • b = 1 against b¹ 1.
   using the t test. How many degrees of freedom apply in this case ?
   State your conclusions. Present and explain your calculations in such a way that I can determine what you did wrong if the answer is wrong.
3. The company's CEO suspects that store number 26 is under-performing relative to the other 25 stores. To test that,
   1. Re-estimate the regression model involved using the data of stores j = 1,...,25 only.
   2. Forecast the value of Y₂₆ for store number 26.
   3. Assuming that the errors U_j are normally distributed with zero expectation and variance s², determine the 90% confidence interval of the forecast of Y₂₆.
      Show how you have calculated this interval.
   4. What is your conclusion?

(*) Click on the link, and save the file as a text file (*.TXT) on your hard disk via the "Save as .." option of your web browser.

(**) If you use Internet Explorer and you click on the link the file will be automatically imported in Excel. Then use the "Save as .." option of Excel to save the file on your hard disk. Netscape and Mozilla Firefox will display the file as a text file. Therefore, if you use Netscape or Mozilla Firefox follow the procedure under (*).