Question

A local store developed a multiplicative time-series model to forecast its revenues in future quarters, using quarterly data on its revenues during the 5-year period from 2008 to 2012. The following is the resulting regression equation: log10 = 6.102 + 0.012 X - 0.129 Q1 - 0.054 Q2 + 0.098 Q3 where is the estimated number of contracts in a quarter X is the coded quarterly value with X = 0 in the first quarter of 2008 Q1 is a dummy variable equal to 1 in the first quarter of a year and 0 otherwise Q2 is a dummy variable equal to 1 in the second quarter of a year and 0 otherwise Q3 is a dummy variable equal to 1 in the third quarter of a year and 0 otherwise To obtain a fitted value for the fourth quarter of 2009 using the model, which of the following sets of values should be used in the regression equation?1. In testing the significance of the coefficient of X in the regression equation (0.012) which has a p-value of 0.02. Which of the following is the best interpretation of this result? a. The quarterly growth rate in revenues is significantly different from 0%. b. The quarterly growth rate in revenues is not significantly different from 0%. c. The quarterly growth rate in revenues is significantly different from 1.2%. d. The quarterly growth rate in revenues is not significantly different from 1.2%. e. The quarterly growth rate in revenues is significantly different from 1.2% 2. using the regression equation, the forecast for the revenues in the fourth quarter of 2004 is:______ a. 6,426 b. 2,666,858 c. 6,638 d. 2,741,574 e. 6,414

Answer 1

The quarterly growth rate in revenues is significantly different from 1.2%.

b. 2,666,858

Explanation:

Given that:

The regression equation can be represented as :

`log_(10) \hat Y= 6.102+0.012 X - 0.129 Q_1 - 0.054 Q_2 + 0.098 Q_3`

In testing the significance of the coefficient of X in the regression equation (0.012) which has a p-value of 0.02.

The null and alternative hypothesis can be stated as;

`H_0:` The quarterly growth rate in revenues is not significantly different from 1.2%.

`H_a:` The quarterly growth rate in revenues is significantly different from 1.2%.

The decision rule is to reject the null hypothesis if the p-value is less than 0.05.

From above ; the p-value = 0.02 which is less than 0.05.

Conclusion:

Thus; we reject the null hypothesis and accept the alternative hypothesis. i.e

The quarterly growth rate in revenues is significantly different from 1.2%.

b.

Since
`Q_1=Q_2=Q_3 = 0` ; X = 27

Thus ;

`log_(10) \hat Y= 6.102+0.012 X - 0.129 Q_1 - 0.054 Q_2 + 0.098 Q_3`

`log_(10) \hat Y= 6.102+0.012 (27)`

`\hat Y=10^( 6.102+0.012 (27) )`

`\hat Y =` 2666858.665

`\hat Y =` 2,666,858