Liner Regression
The calculations for our sample size n = 10 are described below. The linear regression model is y = a + bx
Table:
|
Distance x miles
|
Time y mins
|
xy
|
x2
|
y2
|
|
3.5
|
16
|
56.0
|
12.25
|
256
|
|
2.4
|
13
|
31.0
|
5.76
|
169
|
|
4.9
|
19
|
93.1
|
24.01
|
361
|
|
4.2
|
18
|
75.6
|
17.64
|
324
|
|
3.0
|
12
|
36.0
|
9.0
|
144
|
|
1.3
|
11
|
14.3
|
1.69
|
121
|
|
1.0
|
8
|
8.0
|
1.0
|
64
|
|
3.0
|
14
|
42.0
|
9.0
|
196
|
|
1.5
|
9
|
13.5
|
2.25
|
81
|
|
4.1
|
16
|
65.6
|
16.81
|
256
|
|
Σx = 28.9
|
Σy = 136
|
Σxy = 435.3
|
Σx2 = 99.41
|
Σy2= 1972
|
The Slope b = {(10 * 435.3) - (28.9 * 136)}/ {(10 * 99.41) - (28.9)2} = 2.66
And the intercept a = {136 - (2.66 * 28.9)}/10 = 5.91
Now we insert these values in the linear model describing as
y = 5.91 + 2.66x Or
Delivery time (mins) = 5.91 + 2.66 delivery distance in miles
The slope of the regression line is the estimated number of minutes per mile required for a delivery. The intercept is the estimated time to prepare for the journey and to deliver the goods that is the time required for each journey other than the actual traveling time.