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
20	226.8
21.5	241.4
23	258.2
24.5	277.8
26	297.8
27.5	305.6
29	328.9

Answer:
Volume = ? x+ ? ( where x is the grams of the unknown metal )

Answer 1

X	Y	(x-x̅)²	(y-ȳ)²	(x-x̅)(y-ȳ)
20	226.8	20.25	2484.31	224.2929
21.5	241.4	9	1242.059	105.7286
23	258.2	2.25	340.139	27.66429
24.5	277.8	0	1.33898	0
26	297.8	2.25	447.6247	31.73571
27.5	305.6	9	838.5161	86.87143
29	328.9	20.25	2730.809	235.1571

	ΣX	ΣY	Σ(x-x̅)²	Σ(y-ȳ)²	Σ(x-x̅)(y-ȳ)
total sum	171.5	1936.5	63	8084.797	711.45
mean	24.5	276.642857	SSxx	SSyy	SSxy

sample size ,   n =   7          
here, x̅ =   24.5       ȳ =   276.6428571  
                  
SSxx =    Σ(x-x̅)² =    63          
SSxy=   Σ(x-x̅)(y-ȳ) =   711.45          
                  
slope ,    ß1 = SSxy/SSxx =   11.29286          
                  
intercept,   ß0 = y̅-ß1* x̄ =   -0.03214          
                  
so, regression line is   Ŷ =   -0.0321   +   11.2929   *x
volume =11.293X - 0.032  ( where x is the grams of the unknown metal )