Question

Let Y = sales in one of 25 territories, X1=advertising in territory, X2=bonuses paid in territory. There is also coding scheme for regions:

Region X3 X4
South 1 0
West 0 1
Midwest 0 0

The regression equation is:
ŷ=435 + 1.37X1 + 0.975X2 - 258X3 - 210X4

3)Estimate the sales for West region if Advertising=200, Bonus=100.

Answer 1

To estimate the sales for the West region given Advertising (
X
1
X1) = 200 and Bonus (
X
2
X2) = 100, we'll use the regression equation provided:

y
^
=
435
+
1.37
X
1
+
0.975
X
2
−
258
X
3
−
210
X
4
y
^
​
=435+1.37X1+0.975X2−258X3−210X4

Since the West region is coded as
X
3
=
0
X3=0 and
X
4
=
1
X4=1, we will substitute these values into the equation and calculate the estimated sales (
y
^
y
^
​
).

y
^
=
435
+
1.37
×
200
+
0.975
×
100
−
258
×
0
−
210
×
1
y
^
​
=435+1.37×200+0.975×100−258×0−210×1

Now, perform the calculations:

y
^
=
435
+
274
+
97.5
−
0
−
210
y
^
​
=435+274+97.5−0−210
y
^
=
606.5
y
^
​
=606.5

So, the estimated sales for the West region, given Advertising = 200 and Bonus = 100, is approximately 606.5.