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
x^{2}
y^{2}
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
64
14
42.0
196
1.5
9
13.5
2.25
81
4.1
65.6
16.81
Σx = 28.9
Σy = 136
Σxy = 435.3
Σx^{2 = }99.41
Σy^{2= }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.