Question

Perform linear regression using the known solutions to find the concentrations of the unknown solutions

concentration (mg/L)	absorbance
0.00	0.181
1.00	0.344
2.00	0.661
3.00	0.824
4.00	1.141
5.00	1.304
6.00	1.621
?	0.561
?	0.892
?	1.526

Answer 1

Concentration = X mg/L

Absorbance = Y

Y = a + b X

a = (Σy Σx² – Σx Σxy) / (n Σx² – (Σx)²)

b = (n Σxy – Σx Σy) / (n Σx² – (Σx)²)

n = 7

S No.	x	y	xy	x2
1	0	0.181	0	0
2	1	0.344	0.344	1
3	2	0.661	1.322	4
4	3	0.824	2.472	9
5	4	1.141	4.564	16
6	5	1.304	6.52	25
7	6	1.621	9.726	36
∑	21	6.076	24.948	91

a = 0.148

b = 0.24

A = 0.148 + 0.24 * Concentration

(i)

A = 0.561

Concentration of unknown = (0.561 – 0.148)/ 0.24

= 1.72 mg/L

(ii)

A = 0.892

Concentration of unknown = (0.892 – 0.148)/ 0.24

= 3.1 mg/L

(iii)

A = 1.526

Concentration of unknown = (1.526 – 0.148)/ 0.24

= 5.74 mg/L