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 expresses mass as a function of the volume.

grams	Volume in ml
14	161.9
16.5	189
19	215.5
21.5	248.7
24	272.2
26.5	303.5
29	335.4

A) Write the linear regression equation for the data in the chart.

Volume = x+ where x is the grams of the unknown metal. Round your answers to 3 decimal places

B) If the mass of an unknown metal is 12, using your un-rounded regression equation find its predicted volume. Round your answer to 1 decimal place.    mL

Answer 1

Solution:

X	Y	XY	X^2	Y^2
14	161.9	2266.6	196	26211.61
16.5	189	3118.5	272.25	35721
19	215.5	4094.5	361	46440.25
21.5	248.7	5347.05	462.25	61851.69
24	272.2	6532.8	576	74092.84
26.5	303.5	8042.75	702.25	92112.25
29	335.4	9726.6	841	112493.16

n	7
sum(XY)	39128.80
sum(X)	150.50
sum(Y)	1726.20
sum(X^2)	3410.75
sum(Y^2)	448922.80

,

So ,

b = 11.5171 and a = -1.0186

A) Write the linear regression equation for the data in the chart.

The equation of the regression line is

= bx + a

= 11.517 * x + (-1.019)

i.e.

Volume = 11.517 * x + (-1.019)

B) If the mass of an unknown metal is 12, using your un-rounded regression equation find its predicted volume. Round your answer to 1 decimal place.    mL

Put x = 12 in the regression equation.

Volume = [ 11.517 * 12] + (-1.019)

Volume = 137.2