A manufacturer of copying machines wishes to predict the number of copiers sold
ID: 2909682 • Letter: A
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
X1=0 if Region A
X1= 1 if other
X1= 1if Region A
X2= 1 if other
X1= 1if Region A
X1= 0 if other
X1=1if Region A
X2= 0 if other
The hypothesis to test whether these is a difference in sales among the regions
H0: beta1=beta2<0
H1: beta1=beta2>=0
H0: beta1=beta2=0
H1: At least one beta not = 0
H0: beta1>beta2
H1: beta1<=beta2
H0: beta1< beta2
H1: beta1>=beta2
The value of the F test statistic to conduct the hypothesis test, to two decimal places, is:
A.X1=0 if Region A
X1= 1 if other
X1= 1if Region A
X2= 1 if other
X1= 1if Region A
X1= 0 if other
X1=1if Region A
X2= 0 if other
Explanation / Answer
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
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