ou are the accountant for an economy lodging hotel in suburban Dallas. Your boss asked you to estimate the cost function for your property. Your hotel has only one output: the provision of hotel rooms for overnight stays. The 118-room hotel is a two-story wood building with exterior room access. Download Data.xlsx and Temperature_Data.xlsx on Canvas. The former contains eight years of monthly data for the years 2011-2018. Panel A of Table 1 lists the variable names and a brief description of each variable. The file Temperature_Data.xlsx contains monthly temperature data for the same timeframe. Heating degree days (HDD) and cooling degree days (CDD) are measures that assess the energy required to heat (HDD) and cool (CDD) a building. HDD and CDD are, respectively, the number of days the average temperature is below, or above, 65F (degrees Fahrenheit). Finally, the U.S. Bureau of Labor Statistics estimates consumer prices monthly; Table 2 contains the average annual consumer price index (CPI) youll need to adjust your cost figures for inflation. While it is (mostly) possible to complete this project using Excel, a statistical software package (R, Python, etc.) is highly preferred. Most tests of regression assumptions can be done in Excel, but few of them are automatic manual calculations in Excel are tedious and error prone. On the other hand, Python and R are modern programming languages that are the languages of choice in data analytics. Further, many universities now make learning advanced programming a requirement (e.g., the University of Waterloo and the University of Illinois). Finally, employers are seeking early career accountants that understand technology and can code and program across emerging technology platforms. Required 1. To have enough observations to use multiple regression analysis, data must be collected over a number of years. One of two issues that arise when analyzing data over long time periods is inflation. Inflation causes the value of money to differ across time. This means that the prices of inputs (e.g., electricity and supplies) change (usually rise) over time. It is likely youve experienced a change in the price of goods. For example, a pound of ground beef averaged $3.60 per pound in 2012. Today, the national average price is $4.56 per pound an increase of 27%, or 2.4% annually. This means that regressing spending in actual dollars onto the cost driver produces a cost function model that is meaningless. The solution lies in using a consumer price index: You adjust older amounts to reflect their the most recent value. Using the data in Table 2, adjust total expenses (TotalCost) so all amounts are in 2018 dollars (i.e., with inflation, older amounts become larger). 2. Plot the relationship between total expenses and rooms rented. Do costs behave as you expect? Are there unusual observations? 3. Estimate your hotels cost function using linear regression. That is, regress TotalCost onto Rentals. What is the monthly cost equation? Assess your model in terms of economic plausibility and goodness of fit. Also assess the assumptions behind linear regression modeling (i.e., heteroskedasticity, normality of the residuals and serial autocorrelation). 2 2022 by James Hesford 4. Plot TotalCost versus time. This is best done with separate box plots for each year, placed next to one another. If you observe shifts in spending from year to year, you most likely have to add variables to capture the effect of changes in discretionary fixed spending. (What do you think this means?) Add dummy variables for each year to your regression model. A dummy variable is a variable that has a value of 1 when some criteria is met, and is 0 when the criteria is not met. For example, you want a dummy variable to represent the year 2012. You create a new variable, say d2012, that is 0 for all observations (i.e., rows) for which the year is not 2012, but is 1 when the year is 2012. 5. Add the temperature and yearly dummy variables to your regression model. What is the hotels cost function? What is the interpretation of the dummy variables coefficients? Why (or why not) do you think the dummy variables should be added to the model? Assess the model in terms of economic plausibility and goodness of fit. 6. Oftentimes there are unusual observations in the data that are extreme values in terms of your dependent variable (called outliers), while other data points may be extreme in terms of the independent variable(s) (called influential observations). Outliers reduce your r-square (i.e., the ability to explain variation in the dependent variable) and can change the slope of the regression coefficients (i.e., tilt the regression line such that marginal cost is different than a model without these unusual observations). Using standardized residuals, drop observations with a standardized residual greater than an absolute value of 3. Re-estimate the cost function and assess your new model. 7. If any of the regression coefficients are implausible, remove them from your model and estimate the revised regression model. Do not forget to thoroughly assess any new model (i.e., normality of residuals, serial autocorrelation and heteroskedasticity) 8. Compare your regression models. Select the model you believe is most appropriate and provide arguments in support of your choice. 9. Finally, write up a report you will submit to your manager (or client). Make sure to double- check your work and ensure that your report appears professional.