Suppose a savings and loan association wants to forecast the delinquency rate on home mortgages. Using monthly data, the following trend model is estimated DR. = a+ bt where DR. = the percentage of mortgage payments delinquent in time period t, and t = 1,..,48 (January 2007 through December 2010). The following estimation results are obtained DEPENDENT DRT R-SQUARE F-RATIO P-VALUE ON F VARIABLE: OBSERVATIONS: 48 0.7982 181.93 0.0001 PARAMETER STANDARD VARIABLE T-RATIO P-VALUE ESTIMATE ERROR INTERCEPT 2.60 0.74 3.51 0.0010 T 0.030 0.010 3.00 0.0043 a. Does this estimate indicate a significant upward trend in the delinquency rate on home mortgages? In the space below, perform the appropriate t-test at the 5 percent significance level b. Perform an F-test to determine if the model is statistically significant at the 5 percent level of significance. c. Calculate the predicted delinquency rates for January 2011 and March 2011. DRJan2011 = percent DRMar2011= percentont Paragraph Drawing Editing The trend analysis above indicates that the delinquency rate is rapidly becoming a serious problem for this savings and loan. A management consultant suggests that the trend analysis may be overstating the upward trend because it fails to account for the fact that the months of December and January are consistently much worse months than the rest. The consultant suggests estimating the following model: DR, = a + bt + cD where D is equal to one for the months of December and January, and zero otherwise. The estimation results are: DEPENDENT VARIABLE: DRT R-SQUARE F-RATIO P-VALUE ON F OBSERVATIONS: 48 0.9876 1794.0 0.0001 VARIABLE PARAMETER STANDARD ERROR T-RATIO P-VALUE ESTIMATE INTERCEPT 2.200 0.780 2.82 0.0071 T 0.018 0.004 4.50 0.0001 D 0.810 0.210 3.86 0.0004 H HFORE Paragraph Drawing d. Does the new model indicate a significant upward trend in the delinquency rate? Perform the appropriate t-test. e. Perform a t-test to determine whether December and January are significantly worse months for mortgage payments. f. Predict the delinquency rates for January 2011 and March 2011 DR Jan2011 percent DR Mar2011- percent g. Compare your forecasts in parts c and f. Explain why they differ