Question

A steel rod is subjected to stress. The tensile strength of the rod at different values of the stress are

recorded. Find a relation between the tensile strength and the stress. The data is given below:

Stress (kg): 10 9 7 8 11

Tensile strength: 6 3 2 4 5

Also predict the tensile strength at a stress of 5 kg

Answer 1

Least square method:

y = mx + c

m = slope

c = intercept

$m = \frac{\sum xy - \frac{\sum x \sum y}{n}}{\sum x^2 - \frac{(\sum x)^2}{n}} \\ = \frac{188 - \frac{45 \times 20}{5}}{415 - \frac{(45)^2}{5}} \\ = 0.80 \\ c = \frac{\sum y – m \sum x}{n} \\ = \frac{20 -0.57 \times 45}{5} \\ = -1.13 \\ y = 0.8x -1.13 \\ y(5) = 0.8 \times 5 -1.13 = 2.87$