Question

least squares to fit a straight line

Pre-lab A-3 Least Squares Fit to a Straight Line Read lab A-3: Least squares fit to a straight line. A set of data is given in the following table and plotted on the right: x(s) y (m) Lab 3 exercise 27 Use the graph on the right to calculate the slope and the intercept of the line. 1 2 3 4 5 Slope Intercept Use equations (6) in the lab manual to calculate so, S1, S2, S3, and se. Do not forget units. = (1+2+3+ 4) = x} = (1? + 2 + 32 + 4) = s = 3n-(6+7+8+ 9m = y = (1 x 6+2 x 7+3 8+4 x 9)ms = Then calculate the slope of the line by using Equation (8) 5450-55 S250-s and the intercept by using Equation (9) b= 289-5451 S25o-s Do your results agree with what you calculated form the graph? A-3P.1 December 14, 2017

Answer 1

Values of s0 s1 s2 s3 and s4 is already given as expression in the question.

We can calculate the above values easily by simple addition

s0= 4

s1=1+2+3+4 = 10

s2= 30

s3=6+7+8+9 = 30

s4=1X6 + 2X7 + 3X8 + 4X9 = 80

To find slope(m) and intercept(b) we just have to substitute the values given

m = (s₄Xs₀-s₃Xs₁)/(s₂Xs₀-s₁²) = (80X4 - 30X10)/ (30X4 - 10²) = 20/20 =1

b= (s₂Xs₃-s₄Xs₁)/(s₂Xs₀-s₁²) = (30X30-80X10)/(30X4-10²) = 100/20 = 5

Equation of line y=mx+ b => y=x+5

Slope (m)= 1

Intercept(b) = 5