Question

A manufacturer of copying machines wishes to predict the number of copiers sold per week based on previous sales in each of three regions: Region A, Region B, and Region C. How many dummy variables should be used to represent the qualitative variable - sales region?

Suppose a regression model was fit to n=25 data points with the following results

                         ? = 62 - 4X₁ + 11X₂   MSR=275   MSE=50

_{If we decide to use the variable} X₁ to represent Region A, which of the following structures must be used to indicate this

	A.	X1=0 if Region A X1= 1 if other
	B.	X1= 1if Region A X2= 1 if other
	C.	X1= 1if Region A X1= 0 if other
	D.	X1=1if Region A X2= 0 if other

The hypothesis to test whether these is a difference in sales among the regions

	A.	H0: beta1=beta2<0 H1: beta1=beta2>=0
	B.	H0: beta1=beta2=0 H1: At least one beta not = 0
	C.	H0: beta1>beta2 H1: beta1<=beta2
	D.	H0: beta1< beta2   H1: beta1>=beta2

The value of the F test statistic to conduct the hypothesis test, to two decimal places, is:

Answer 1

a) If a qualitative variable is used with c categories then c-1 dummy variables need to be used.

The Sales variable has 3 categories hence 2 dummy variables need to be used.

b) If variable X1 is used to represent Region A then, we must use the following structure to indicate this.

Answer c. X1= if Region A and X1= 0 if Other

The dummy variable for which Y needs to be calculated is represented as 1 while the others are set to 0.

c) The hypothesis to test whether there is a difference in sales among regions is

Answer b.  

H0: beta1=beta2=0
H1: At least one beta not = 0

d) F statistic = MSR / MSE = 275/50 = 5.5