CHAPTER 13 Simple Linear Regression

520 CHAPTER THIRTEEN Simple Linear Regression
COMPUTATIONAL FORMULA FOR THE Y INTERCEPT, b 0
b0 = Y − b1X
(13.4)
where
Y
=
n
∑
i=
1
n
Y
i
X =
n
∑
i=
1
n
X
i
EXAMPLE 13.3 COMPUTING THE Y INTERCEPT, b 0
, AND THE SLOPE, b 1
Compute the Y intercept, b 0
, and the slope, b 1
, for the Sunflowers Apparel data.
SOLUTION Examining Equations (13.3) and (13.4), you see that five quantities must be calculated
to determine b 1
and b 0
. These are n, the sample size;
n
∑Y i
i=
1
n
2
∑ X i
i=1
, the sum of the X values;
, the sum of the Y values; , the sum of the squared X values; and XY, the sum
of the product of X and Y. For the Sunflowers Apparel data, the number of square feet is used to
predict the annual sales in a store. Table 13.2 presents the computations of the various sums
needed for the site selection problem, plus
used to compute SST in Section 13.3.
n
2
∑Y i
i=1
n
∑ X i
i=
1
i=
1
, the sum of the squared Y values that will be
n
∑
i
i
TABLE 13.2
Computations for the
Sunflowers Apparel
Data
Square Annual
Store Feet (X ) Sales (Y ) X 2 Y 2 XY
1 1.7 3.7 2.89 13.69 6.29
2 1.6 3.9 2.56 15.21 6.24
3 2.8 6.7 7.84 44.89 18.76
4 5.6 9.5 31.36 90.25 53.20
5 1.3 3.4 1.69 11.56 4.42
6 2.2 5.6 4.84 31.36 12.32
7 1.3 3.7 1.69 13.69 4.81
8 1.1 2.7 1.21 7.29 2.97
9 3.2 5.5 10.24 30.25 17.60
10 1.5 2.9 2.25 8.41 4.35
11 5.2 10.7 27.04 114.49 55.64
12 4.6 7.6 21.16 57.76 34.96
13 5.8 11.8 33.64 139.24 68.44
14 3.0 4.1 9.00 16.81 12.30
Totals 40.9 81.8 157.41 594.90 302.30