Question #129

The R2 is the ratio of the explained variation to the total variation. (Module 1.2, LOS 1.d) Manuel Mercado, CFA has performed the following two regressions on sales data for a given industry. He wants to forecast sales for each quarter of the upcoming year. Model ONE Regression Statistics Multiple R 0.941828 R2 0.887039 Adjusted R2 0.863258 Standard Error 2.543272 Observations 24 Durbin-Watson test statistic = 0.7856 ANOVA df SS MS F Significance F Regression 4 965.0619 241.2655 37.30006 9.49E−09 Residual 19 122.8964 6.4682 Total 23 1087.9583 Coefficients Standard Error t-Statistic Intercept 31.40833 1.4866 21.12763 Q1 −3.77798 1.485952 −2.54246 Q2 −2.46310 1.476204 −1.66853 Q3 −0.14821 1.470324 −0.10080 TREND 0.851786 0.075335 11.20848 Model TWO Regression Statistics Multiple R 0.941796 R2 0.886979 Adjusted R2 0.870026 Standard Error 2.479538 Observations 24 Durbin-Watson test statistic = 0.7860 df SS MS F Significance F Regression 3 964.9962 321.6654 52.3194 1.19E−09 Residual 20 122.9622 6.14811 Total 23 1087.9584 Coefficients Standard Error t-Statistic Intercept 31.32888 1.228865 25.49416 Q1 −3.70288 1.253493 −2.95405 Q2 −2.38839 1.244727 −1.91881 TREND 0.85218 0.073991 11.51732 The dependent variable is the level of sales for each quarter, in $ millions, which began with the first quarter of the first year. Q1, Q2, and Q3 are seasonal dummy variables representing each quarter of the year. For the first four observations the dummy variables are as follows: Q1:(1,0,0,0), Q2:(0,1,0,0), Q3:(0,0,1,0). The TREND is a series that begins with one and increases by one each period to end with 24. For all tests, Mercado will use a 5% level of significance. Tests of coefficients will be two-tailed, and all others are one-tailed.