A researcher measures the expansion of concrete due to a process call the alkali

Question

A researcher measures the expansion of concrete due to a process call the alkali-silica reaction. Measurements are taken in both the horizontal (x) and vertical (y) direction and are given in the table below. The expansion is measure in parts per hundred thousand Horizontal (x) 20 15 43 5 18 2432 10 21 Vertical (y) 58 58 55 80 58 68 57 69 63 a. Compute the least-squares line for predicting vertical expansion from horizontal expansion Compute 95% confidence intervals on the slope and the y-intercept. b.

Explanation / Answer

matlab code

close all

clear

clc

% y = mx + c

% [x, 1]*[m; c] = y

% A = [x, 1]

% y = vertical values

% x = horizontal values

% [20 1;

% 15 1;

% 43 1;

% 5 1;

% 18 1;

% 24 1;

% 32 1;

% 10 1;

% 21 1]*[m; c] = [58 58 55 80 58 68 57 69 63]';

A = [20 1;

15 1;

43 1;

5 1;

18 1;

24 1;

32 1;

10 1;

21 1];

y = [58 58 55 80 58 68 57 69 63]';

x = (inv(A'*A)*A')*y;

m = x(1); c = x(2);

fprintf('Solution: Slope = %f, Intercept = %f ',m,c);

fprintf(' 95 Percent Confidence Interval for slope = %f to %f, and intercept is %f to %f ', 1.05*m, 0.95*m, 0.95*c, 1.05*c);

output

Solution:

Slope = -0.496785, Intercept = 73.266181

95 Percent Confidence Interval for slope = -0.521625 to -0.471946, and intercept is 69.602872 to 76.929490

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