Question

An unknown metal has been found and the following experimental results have been tabulated in the table below. The table contains the grams of the unknown metal and the volume in milliliters of water displacement. Find a linear model that express mass as a function of the volume.

Round your answers to 3 decimal places

grams	Volume in ml
13	144.5
14.5	162.8
16	183.3
17.5	202.4
19	211.2
20.5	227.8
22	247

Volume =_________ x+___________  where x is the grams of the unknown metal

Answer 1

grams	Volume in ml
13	144.5
14.5	162.8
16	183.3
17.5	202.4
19	211.2
20.5	227.8
22	247

grams	volume(in ml)	grams*volume(in ml)	grams2	volume(in ml)2
	13	144.5	1878.5	169	20880.25
	14.5	162.8	2360.6	210.25	26503.84
	16	183.3	2932.8	256	33598.89
	17.5	202.4	3542	306.25	40965.76
	19	211.2	4012.8	361	44605.44
	20.5	227.8	4669.9	420.25	51892.84
	22	247	5434	484	61009
Sum =	122.5	1379	24830.6	2206.75	279456.02

=122.5/7​=17.5

=1379/7​=197

=2206.75−122.52/7=63

=279456.02−13792/7=7793.02

=24830.6−122.5×1379/7=698.1

b===11.081

n==197−17.5×11.081=3.0833

Therefore, we find that the regression equation is:

volume(in ml) = 3.0833 + 11.081 grams

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