A consulting firm estimates the following quarterly sales forecasting model The
ID: 3066881 • Letter: A
Question
A consulting firm estimates the following quarterly sales forecasting model The equation is estimated using quarterly data from 2005-2015 (-1.,., 43). The variable D is a dummy variable for the third quarter where: D 1 in the third quarter, and 0 otherwise. The results of the estimation are E QT R SQUARE F-RATIO P.VALUE ONF 0.0001 T-RATIO P-VALUE 2.41 3.38 2.82 OBSERVATIONS: 430.8644 127.5 PARAMETER STANDARD ERROR 9.32 0.55 0.71 VARIABLE ESTIMATE 22.5 1.86 -3.2 0.0201 0.0016 0.0075 INTERCEPT 1. Given the above, at the 1 percent level of significance, is there a statistically significant trend in sales? a. Yes, because 0.0016 0.01. b. No, because 0.0016> 0.001. c. Yes, because 0.55> 0.01. d. Yes, because 1.86 0.01. e. both c and d 2. Given the above, these estimates indicate that the third quarter change in sales is a. 22.5 units higher in the third quarter than in the other three quarters b. 1.86 units higher in the third quarter than in the other three quarters. C. 3.2 units lower in the third quarter than in the other three quarters. d. 3.2 units higher in the third quarter than in the other three quarters. 3. Using the estimated trend line above, what is the predicted level of sales in 2016/? a 110.06 b. 106.20 104.34 d. 102.2 e. none of the aboveExplanation / Answer
1. Answer: a. Yes, because 0.0016 < 0.01
The p-value for the parameter tells whether the parameter has significant effect on the dependent variable. If the p-value is less than the significance level, then the parameter has effect. Here, the ANOVA output gives us that the p-value for T is 0.0016 which is less than the desired significance of 0.01.
Option b is incorrect because our desired significance level is 1% = 0.01, not 0.001.
Options c, d, and e are incorrect because the value and/or the standard error for that parameter have no relationship with the desired significance level.
2. Answer: c. 3.2 units lower in the third quarter than in the other three quarters.
Regression tells us that the parameter estimate for D is -3.2. The value for D is 1 for the third quarter and 0 for the other quarters. This means that in the third quarter (when D=1), the sales is lower by 3.2 units as compared to other quarters (when D=0).
Options a and b are using the incorrect parameter which has no relation to the quarter change data.
Options d is ignoring the sign of the parameter estimate, leading to an incorrect conclusion.
3. Answer: b. 106.20
The regression equation is Qt = a+bt+cD = 22.5+1.86*t-3.2*D
For 2016I, the value of t will be 45 and the value of D will be 0. So, Qt = 22.5+1.86*45-3.2*0 = 106.2.
Options a, c, and d are incorrect as they do not match this value.
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.