Example
• Given below is a six-monthly timber
demand for houses based on application
for building permits
• Required
Using least square methods to :
(a) Find the y intercept b0
(b) Find the slope (b1
)
(c) Find the predicted model (𝑦ො)
Period
No of
Permits
Timber
Demand
1 30 10
2 45 17
3 52 21
4 47 18
5 55 24
6 50 21
7 46 17
8 40 12
9 38 10
10 29 8
11 37 11
12 40 13
13 44 16
14 51 20
Cont:
Step 1. Expand the Table
Step 2. Find b0 & b1
b1 = ௌௌ
ௌௌ
SSXY =∑ 𝑥𝑖𝑦𝑖
ୀଵ - ∑ ௫ (∑ ௬)
= 9898 -(ସ)(ଶଵ଼) ଵସ
= 9898 -9405.142857 = 492.857143
Ssx = ∑ 𝑥𝑖 2
ୀଵ - ∑ ௫ ଶ
=26870 - ସ ଶ
ଵସ
= 26870 – 26058.2857 =811.714329
So that b1 = ௌௌ
ௌௌ
= 𝟒𝟗𝟐.𝟖𝟓𝟕𝟏𝟒𝟑
𝟖𝟏𝟏.𝟕𝟏𝟒𝟐𝟗
= 0.60718
b0 =𝑦ത - b1𝑥̅
= 15.57142857 – 0.60718(43.14285714) = -10.624105
Step 3. Predicted Model
𝑦ො =b0 + b1Xi or
Period
No of Permits
(x)
Timber
Demand (y) X2 Y2
xy
1 30 10 900 100 300
2 45 17 2025 289 765
3 52 21 2704 441 1092
4 47 18 2209 324 846
5 55 24 3025 576 1320
6 50 21 2500 441 1050
7 46 17 2116 289 782
8 40 12 1600 144 480
9 38 10 1444 100 380
10 29 8 841 64 232
11 37 11 1369 121 407
12 40 13 1600 169 520
13 44 16 1936 256 704
14 51 20 2601 400 1020
SUM: 604 218 26870 3714 9898
Mean of y 15.57142857
Step 3. Predicted Model
𝑦ො =b0 + b1Xi or
𝑦ො = -10.624105 + 0.60718Xi
Therefore, the predicted model for timber demand based on building permits is:
Timber Demand = -10.624105 + 0.60718(No of Permits)
This model can be used to predict the timber demand for houses based on the number of building permits received.