Question

Mist (airborne droplets or aerosols) is generated when metal-removing fluids are used in machining operations to cool and lubricate the tool and workpiece. Mist generation is a concern to OSHA, which has recently lowered substantially the workplace standard. An article gave the accompanying data on x = fluid-flow velocity for a 5% soluble oil (cm/sec) and y = the extent of mist droplets having diameters smaller than 10 µm (mg/m³):

x	90	177	190	354	361	442	963
y	0.38	0.60	0.50	0.66	0.62	0.69	0.98

(b) What proportion of observed variation in mist can be attributed to the simple linear regression relationship between velocity and mist? (Round your answer to three decimal places.)

Answer 1

(b)

Following table shows the calculations:

	X	Y	X^2	Y^2	XY
	90	0.38	8100	0.1444	34.2
	177	0.6	31329	0.36	106.2
	190	0.5	36100	0.25	95
	354	0.66	125316	0.4356	233.64
	361	0.62	130321	0.3844	223.82
	442	0.69	195364	0.4761	304.98
	963	0.98	927369	0.9604	943.74
Total	2577	4.43	1453899	3.0109	1941.58

It shows that 0.922 of observed variation in mist can be attributed to the simple linear regression relationship between velocity and mist.