Question #55

Influential observations are those that, when excluded, cause a significant change to the model coefficients. Observations 10 (D = 0.389) and 19 (D = 0.517) satisfy this criteria. (Module 1.4, LOS 1.k) Toni Williams, CFA, has determined that commercial electric generator sales in the Midwest U.S. for Self-Start Company is a function of several factors in each area: the cost of heating oil, the temperature, snowfall, and housing starts. Using data for the most currently available year, she runs a cross-sectional regression where she regresses the deviation of sales from the historical average in each area on the deviation of each explanatory variable from the historical average of that variable for that location. She feels this is the most appropriate method since each geographic area will have different average values for the inputs, and the model can explain how current conditions explain how generator sales are higher or lower from the historical average in each area. In summary, she regresses current sales for each area minus its respective historical average on the following variables for each area. The difference between the retail price of heating oil and its historical average. The mean number of degrees the temperature is below normal in Chicago. The amount of snowfall above the average. The percentage of housing starts above the average. Williams used a sample of 26 observations obtained from 26 metropolitan areas in the Midwest U.S. The results are in the tables below. The dependent variable is in sales of generators in millions of dollars. Observations where Cook's D > √ = √ = 0.3873. k n 3 20 Coefficient Estimates Table Variable Estimated Coefficient Standard Error of the Coefficient Intercept 5.00 1.850 $ Heating Oil 2.00 0.827 Low Temperature 3.00 1.200 Snowfall 10.00 4.833 Housing Starts 5.00 2.333 Analysis of Variance Table (ANOVA) Source Degrees of Freedom Sum of Squares Mean Square Regression 4 335.20 83.80 Error 21 606.40 28.88 Total 25 941.60 Table of the F-Distribution Critical values for right-hand tail area equal to 0.05 Numerator: df1 and Denominator: df2 df1 df2 1 2 4 10 20 1 161.45 199.50 224.58 241.88 248.01 2 18.513 19.000 19.247 19.396 19.446 4 7.7086 6.9443 6.3882 5.9644 5.8025 10 4.9646 4.1028 3.4780 2.9782 2.7740 20 4.3512 3.4928 2.8661 2.3479 2.1242 One of her goals is to forecast the sales of the Chicago metropolitan area next year. For that area and for the upcoming year, Williams obtains the following projections: heating oil prices will be $0.10 above average, the temperature in Chicago will be 5 degrees below normal, snowfall will be 3 inches above average, and housing starts will be 3% below average. In addition to making forecasts and testing the significance of the estimated coefficients, she plans to perform diagnostic tests to verify the validity of the model's results.