Question

The NFL Scouting Combine is an event at which football scouts evaluate the abilities of some top college prospects. Following are heights in inches and weighs in pounds for some of the quarterbacks at the 2013 Combine. Compute the slope b 1 least-square regression line for predicting weight from height. Round your answer to 3 decimal places.

Height (x) 75 78 75 79 75 76 77 77 74 75 74 76 75 74

weight (y) 227 232 231 225 240 225 226 237 227 219 218 237 226 215

=

Answer 1

We are given the following data and are asked to calculate the slope b1 least square regression line for predicting weight from height rounding off to 3 decimal places.

Height(x)	Weight(y)
75	227
78	232
75	231
79	225
75	240
76	225
77	226
77	237
74	227
75	219
74	218
76	237
75	226
74	215

The formula for calculating the slope coefficient is

To calculate slope of the regression we prepare the calculation as follows:

xi			yi
75	-0.714	0.510	227	-0.5	0.357
78	2.286	5.226	232	4.5	10.287
75	-0.714	0.510	231	3.5	1.785
79	3.286	10.798	225	-2.5	-8.215
75	-0.714	0.510	240	12.5	-8.925
76	0.286	0.082	225	-2.5	-0.715
77	1.286	1.654	226	-1.5	-1.929
77	1.286	1.654	237	9.5	12.217
74	-1.714	2.938	227	-0.5	0.857
75	-0.714	0.510	219	-8.5	6.069
74	-1.714	2.938	218	-9.5	16.283
76	0.286	0.082	237	9.5	2.717
75	-0.714	0.510	226	-1.5	1.071

74 -1.714 2.938 215 -12.5 21.425

,

Therefore,

Hence slope coefficient b1=1.727