Question

An article discusses methods to reduce transportation costs while satisfying demands. In one study, the percent demand that is unmet (y) and the percent of vehicle capacity (x) needed to meet the expected demand were recorded for 15 different scenarios. The results are presented in the following table.

x	y
82	0.6
92	0
95	0.7
87	1.3
90	0.8
94	1.1
92	0.9
97	1.2
97	1.3
89	0.2
88	0.8
96	1.4
95	0.9
86	1.4
95	0.4

Note: This problem has a reduced data set for ease of performing the calculations required. This differs from the data set given for this problem in the text.

Compute the least-squares line for predicting unmet demand (y) from vehicle capacity (x). Round the answers to four decimal places.

Predict the unmet demand when the vehicle capacity is 93%. Round the answer to three decimal places.

Answer 1

x: vehicle capacity

y:  unmet demand

Predicted unmet demand :

least-squares line for predicting unmet demand (y) from vehicle capacity (x)

= b_o + b₁x

' 'b_o' indicates the value of y when x=0. It is called y-intercept

'b₁' indicates the slope of the regression line and gives a measure of change of 'y' for a unit change in 'x'

n : Number pairs of observations : sample size = 15

x	y	xy	x2
82	0.6	49.2	6724
92	0	0	8464
95	0.7	66.5	9025
87	1.3	113.1	7569
90	0.8	72	8100
94	1.1	103.4	8836
92	0.9	82.8	8464
97	1.2	116.4	9409
97	1.3	126.1	9409
89	0.2	17.8	7921
88	0.8	70.4	7744
96	1.4	134.4	9216
95	0.9	85.5	9025
86	1.4	120.4	7396
95	0.4	38	9025
=1375	=13	=1196	=126327

Least square line for predicting unmet demand (y) from vehicle capacity (x)

= -0.5255 + 0.0152 x

Predict the unmet demand when the vehicle capacity is 93% i.e substitute x=93 in the above equation

= -0.5255 + 0.0152 x = -0.5255 + 0.0152 * 93 = -0.5255+1.4136=0.88810.888

Answer :

0.888