Question

Longwave (LW) and shortwave (SW) are two appearance measures used in the automotive industry to rate the quality of a paint job. These two measures are generally related. Values for 13 cars are given. Use these data to answer the following:

What value represents the coefficient of correlation between the LW and SW appearances?

LW	SW
10.4	30.5
7.3	28.9
10.5	29.9
6.5	24.2
5.1	23.1
4.2	24.4
7	29
9.4	27.3
6.9	22.8
5.1	21.1
4.2	22
11.4	28.7
10.1	28.7

Group of answer choices

0.8199

0.6723

0.3461

0.124

Answer 1

Solution:

We have to find coefficient of correlation between the LW and SW appearances.

Formula:

where

Thus we need to make following table:

x: LW	y: SW	x^2	y^2	xy
10.4	30.5	108.16	930.25	317.2
7.3	28.9	53.29	835.21	210.97
10.5	29.9	110.25	894.01	313.95
6.5	24.2	42.25	585.64	157.3
5.1	23.1	26.01	533.61	117.81
4.2	24.4	17.64	595.36	102.48
7	29	49	841	203
9.4	27.3	88.36	745.29	256.62
6.9	22.8	47.61	519.84	157.32
5.1	21.1	26.01	445.21	107.61
4.2	22	17.64	484	92.4
11.4	28.7	129.96	823.69	327.18
10.1	28.7	102.01	823.69	289.87

Thus we get:

Thus we get correlation coefficient:

Thus correct option is: 0.8199