A consulting firm estimates the following quarterly sales forecasting model: Q = a - br - CD The equation is estimated using quarterly data from 20101-202011 (r = 1

A linear equation is given that defines the quarterly sales of a consulting firm.

The table gives us the parameter estimates and the t-values and p-values which will be required to answer the respective sub-parts.

We can rewrite the equation using the table as-

a)

To forecast for the year 2020 quarter IV, we need to substitute the values of t and D in the equation above.

Here, t is the number of quarters from 2010 quarter one till the date we are trying to predict. So here it is

t = 44

Also, D = 0 (as we are predicting the fourth quarter and D is zero for all non-second quarters)

So we get,

The answer is option 3.

b)

To check statistical significance at 1% confidence interval (or level of significance) we check the p-values of the variables and whether they are less than 0.01 (1%). The value is significant at 1% level of significance if it is less than 0.01.

The options give us a clue to the right answer. As significance has nothing to do with the parameter estimate, we rule out option 5 and 4. Standard error also does not show significance by itself so option 3 is ruled out. Now we are left with two options.

As the p-value of T is less than 0.01, it is significant and the answer is option1.

c)

The last question asks what the estimated intercept (a) for the thirst quarter will be. Because the intercept does not depend on the quarter or the time period t, it will remain the same ( a = 22.5 from the table). Therefore option 1 is the answer.