Question

Management of a soft-drink bottling company wants to develop a method for allocating delivery costs to customers. Although one cost clearly relates to travel time within a particular route, another cost variable reflects the time required to unload the cases of soft drink at the delivery point. A sample of 20 deliveries within a territory was selected. The delivery times (in minutes) and the number of cases delivered were recorded in the file below.

Customer	Number of cases	Delivery Time
1	52	32.1
2	64	34.8
3	73	36.2
4	85	37.8
5	95	37.8
6	103	39.7
7	116	38.5
8	121	41.9
9	143	44.2
10	157	47.1
11	161	43
12	184	49.4
13	202	57.2
14	218	56.8
15	243	60.6
16	254	61.2
17	267	58.2
18	275	63.1
19	287	65.6
20	298	67.3

a. Use the least squares method to compute the regression coefficients b0 and b1

b. Interpret the meaning of b0 and b1 in this problem

Answer 1

a.

Line of Regression Y on X i.e Y = bo + b1 X
X	Y	(Xi - Mean)^2	(Yi - Mean)^2	(Xi-Mean)*(Yi-Mean)
52	32.1	13900.41	273.076	1948.298
64	34.8	11214.81	191.131	1464.068
73	36.2	9389.61	154.381	1203.983
85	37.8	7208.01	117.181	919.043
95	37.8	5610.01	117.181	810.793
103	39.7	4475.61	79.656	597.083
116	38.5	2905.21	102.516	545.738
121	41.9	2391.21	45.226	328.853
143	44.2	723.61	19.581	119.033
157	47.1	166.41	2.326	19.673
161	43	79.21	31.641	50.063
184	49.4	198.81	0.601	10.928
202	57.2	1030.41	73.531	275.258
218	56.8	2313.61	66.831	393.218
243	60.6	5343.61	143.401	875.373
254	61.2	7072.81	158.131	1057.558
267	58.2	9428.41	91.681	929.733
275	63.1	11046.01	209.526	1521.323
287	65.6	13712.41	288.151	1987.773
298	67.3	16409.61	348.756	2392.268

calculation procedure for regression
mean of X = ∑ X / n = 169.9
mean of Y = ∑ Y / n = 48.625
∑ (Xi - Mean)^2 = 124619.8
∑ (Yi - Mean)^2 = 2514.51
∑ (Xi-Mean)*(Yi-Mean) = 17450.06
b1 = ∑ (Xi-Mean)*(Yi-Mean) / ∑ (Xi - Mean)^2
= 17450.06 / 124619.8
= 0.14
bo = ∑ Y / n - b1 * ∑ X / n
bo = 48.625 - 0.14*169.9 = 24.835
value of regression equation is, Y = bo + b1 X
Y'=24.835+0.14* X          
bo = 24.835
b1= 0.14

b.
value of regression equation is, Y = bo + b1 X
the regression equation is compared to line equation y = mx +c
here, m is slope of the equation
c is the constant
so that, bo = constant = 24.835 = y intercept
b1 =slope of the equation = 0.14
X intercept = -24.835/0.14 =-177.392