Question

1. If the correlation between two variables X and Y is -0.50, then ...

	a.	there is no relationship between the variables.
	b.	there is no linear relationship between the variables.
	c.	there is an inverse relationship between the variables.
	d.	there is a direct relationship between the variables.

2.

Given the following forecast errors: 6, 0, -4 and 2. What is the Average Error?

		4
		1
		12
		3
		14

3.

Given the following data and using exponential smoothing with alpha=50%, the forecast for time 4 is:

Time     Y
1         6
2        12
3         4
4        10

	a.	6.3
	b.	6
	c.	6.6
	d.	6.5

4.

If the Mean Absolute Error of a forecast is equal to one then the forecast is perfectly accurate and contains no error.

True

False

Answer 1

Q1 : there is an inverse relationship between the variables.

The correlation coefficient between 2 variables lies between +1 and -1. If the value is 0, that means there is no relationship between 2 variables. In case the value is non-zero and positive that means there is a direct relationship between the variables. In case the value is non-zero and negative which is the case for this question, that means there is a inverse relationship between the variables. Hence the correct answer is there is an inverse relationship between the variables.

Q2 : 1

Average error is simply the average of all the errors. As there are 4 errors with values 6, 0, -4 and 2, average error is as below

Average Error = (6+0-4+2)/4 = 4/4 = 1

Q3 : 6.5

In exponential smoothing, the forecast for a period is given as below

Forecast for a period = Forecast for previous period+alpha*(Actual for previous period - Forecast for previous period)

The forecast for the first period is considered equal to the actual value and alpha is given as 50% or 0.5 in this case. Hence the forecasts for subsequent periods are as follows

Period 2 Forecast = 6+0.5*(6-6) - 6+0.5*0 = 6

Period 3 Forecast = 6+0.5*(12-6) = 6+0.5*6 = 9

Period 4 Forecast = 9+0.5*(4-9) = 9+0.5*(-5) = 6.5

Hence forecast for period 4 is 6.5

Q4 : False

This statement is false. Mean absolute error is simply the average of absolute values of all the errors. If this is equal to 1, it does not mean that forecast is perfectly accurate. Consider a case where the errors are 1, -2, 0 and 2. Here the mean absolute error is 4/4 = 1. However we can see that there are errors in the forecast and hence the forecast is not perfectly accurate.