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Modelling Business Data

Question 1.

(a) Taking price as the dependent variable and age, area and total as the initial independent variables, obtain an adequate multiple regression model, describing the steps involved in obtaining your model.

Data examination: A price boxplot indicated approximate normality, without outliers.

Examine assumptions: This is a random sample, so I assumed independence (Maxwell & Delaney, 2004). Bivariate scatterplots of price with predictors suggest no non-linear relationships, except some curvature in the price*area graph (Neter, et al., 1996).

Estimate model one: Simultaneous entry of the three predictors yielded a significant model, and showed that my concerns about correlation between area and total (Spearman correlation = 0.714; Lehmann & D'Abrera, 1998) were unfounded. The largest VIF was 2.6, well below the traditional 4.0 threshold (Berry, 1993). However, residual analysis was unsatisfactory. Plotting residuals against predicted values showed a U-shaped pattern, and the histogram of residuals was skewed.

Estimate model two: I replaced area with area squared, producing a better model. The bivariate relation between price and area-squared was linear, the F statistic increased, and the residuals were normally distributed and unrelated to predicted values.

(b) Suppose you are in the technical support section of the estate agency and that you have just developed the model obtained in part (a). Write a short report to your general manager about this model. You should include a description of the model, its likely effectiveness in predicting the selling price of a house, and any reservations you might have about the agency using it in its present form.

Dear NAME,

I have created a regression model of house prices. Regression is a statistical technique for predicting the value of one variable using others - in this case, predicting house values from their age, total number of rooms, and total floor area. This report briefly describes the model, and its potential implications.

The model was highly successful. It suggests that the number of rooms is not an important predictor, but age and area account for 95% of the variance in prices. In other words, for the houses in this sample, knowing the age and total area of the house allows us to make an accurate estimate of its selling price. As you might expect, age decreases the value of the house, while greater total area increases it. I will not present specific details in this initial report, but I will say that the simple formula created by the model provides a potentially powerful tool for estimating the potential market price of a house.

However, the model needs to be used with caution. It is accurate for the data it is based upon, but its applicability to other houses is less certain. For example, the houses in the sample were between 2 and 28 years old, and the same relationship between price and age may not hold for older houses. Consider heritage houses, as one example; age is unlikely to decrease price in such a case. Similarly, the largest house in the sample was 310 m², and it may be that extremely large houses are different as well. Another consideration is time. If fashion changes what homebuyers are looking for, those changes will undermine the accuracy of predictions.

Nonetheless, I am excited about this possibility. We cannot use it indiscriminately; but within its limits, I believe this model provides an important tool for estimating the potential value of a house.

Question 2.

(a) In the context of hypothesis testing regarding one mean, the test (Z or t) may be statistically significant at a particular level (for example 5%) but not significant in a practical sense at all. Illustrate the meaning of this statement by citing an example from an area of business.

ACME and ABC each implement a Total Quality Management (TQM) program to strengthen their market position through a client-centred approach (Barkley & Saylor, 1994). Both firms collect customer input, and make the implicated changes to their internal systems. To evaluate their TQM policy, they survey customer satisfaction before and after implementation.

ACME is a large multinational corporation. It surveyed a random sample of 5,000 customers, and found that average customer satisfaction increased from 3.3 to 3.5 (on a 5-point scale). This change was statistically significant. In contrast, ABC is a small, private firm. It surveyed 10 randomly selected customers, and though it found that average satisfaction increased from 3.3 to 4.8, the change was not statistically significant.

This hypothetical example highlights the difference between statistical significance and practical significance. The statistical power of Acme's large survey made their small, and probably unimportant, change statistically significant. In contrast, ABC's survey found no statistically significant difference, despite a great improvement in satisfaction. This is why effect size may be more important for business than statistical significance (Kenny, 1987).

(b) Trend curve analysis is an example of a forecasting technique used in business. Briefly discuss some of the roles within a large firm or organisation in which statistical forecasting has been found to be useful.

Financial forecasting is the best-known sort. One important instance of this is seasonal variations in production: most industrial outputs are adjusted to reflect seasonal differences in demand (Miron & Beaulieu, 1996). For example, more automobiles are sold in the summer than in the winter. Forecasting thus allows manufacturers to adjust output in response, and avoid summer shortages and excess winter inventory. Without time series-based estimates of demand, production levels would be highly inefficient. Another important example is deflation, where corrections are made to compare dollar values from different times; it would be misleading to compare quantities such as productivity and return in nominal dollars.

However, the utility of forecasting is not limited to financial issues; any time series data may be forecasted. Strategy can be based on forecasts, using techniques such as the balanced scorecard (Kaplan & Norton, 1996). To give a specific example, large pharmaceutical companies track many attributes of drugs in development, and use them to predict the likelihood of each compound's success. These estimates are then used to allocate resources and prioritize projects (Robbins-Roth, 2000). Similar means are used in quality control analyses and error correction.

References

Barkley, B. T. & Saylor, J. H. (1994). Customer driven project management: A new paradigm in total quality implementation. Boston, MA: McGraw-Hill Inc.

Berry, W. D. (1993). Understanding Regression Assumptions. Beverly Hills, CA: Sage.

Kaplan, R. S. & Norton, D. P. (1996). The balanced scorecard: Translating strategy into action. Cambridge, MA: Harvard University Press.

Kenny, D. A. (1987). Statistics for the social and behavioral sciences. Boston, MA: Little, Brown & Company.

Lehmann, E. L. & D'Abrera, H. J. M. (1998). Nonparametrics: Statistical methods based on ranks (2nd ed.). Englewood Cliffs, NJ: Prentice-Hall.

Maxwell, S. E. & Delaney, H. D. (2004). Designing experiments and analyzing data: A model comparison perspective. Mahwah, NJ: Lawrence Erlbaum Associates.

Miron, J. A. & Beaulieu, J. J. (1996). What have macroeconomists learned about business cycles from the study of seasonal cycles? Review of Economics and Statistics, 78, 54-66.

Neter, J., Kutner, M. H., Nachtsheim, C. J., & Wasserman, W. (1996). Applied linear statistical models. Boston, MA: McGraw-Hill.

Robbins-Roth, C. (2000). From alchemy to IPO. Cambridge, MA: Perseus Publishing.

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