Determine times for three variables using Least squares powerfit

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Juan Barragan 2022-4-15

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关闭： Matt J 2023-12-21

Hello, I'm having trouble figuring out the thinking time, braking car time and motorcycle braking time at speeds 20km/hr, 50km/hr, 80km/hr, 100km/hr, 120km/hr and 150km/hr using the least squares power fit method

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Torsten 2022-4-15

In other words:

What is "least-squares powerfit" ?

Juan Barragan 2022-4-17

yes, I've been having difficulty on figuring out the equations for each time

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Answer 1

Ravi 2023-12-21

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Hi Juan Barragan,

I understand you are facing trouble in arriving at equations for the variables. I hope the following approach will be helpful to you.

The least squares power fit method is a technique used to find the best-fitting power function that minimizes the sum of the squared differences between the observed and predicted values.

A power-law relationship is represented by the equation,

y = a * x ^ b

Where a is a coefficient and b is the exponent.

The following function can help you in obtaining the equation.

speed = [30, 45, 60, 75, 90, 120];
thinking = [6, 9, 11, 15, 17, 22];
powerfit(speed, thinking);
Equation: y = 0.2436x^0.9432
y = 0.2436 * (20 ^ 0.9432)
y = 4.1097
function [] = powerfit(x, y) 
    % Perform least squares power fit 
    logx = log(x); 
    logy = log(y); 
    
    % Use polyfit for linear regression on transformed data 
    p = polyfit(logx, logy, 1); 
    
    % Extract coefficients 
    a = exp(p(2));  % Intercept term corresponds to log(a) 
    b = p(1);       % Slope corresponds to exponent b 
    
    % Display results 
    fprintf('Equation: y = %.4fx^%.4f\n', a, b); 
end 

The above function “equation” takes input two arguments “x” and “y” where “x” represents the Speed and “y” can take Thinking, Braking Car and Braking motorcycle.

Once after obtaining the equation, we can find the response variable by simply substituting the Speed value in place of “x” in the obtained equation.

To know more about the “polyfit” function, please refer to the following link.

polyfit - https://www.mathworks.com/help/matlab/ref/polyfit.html

Hope this explanation resolves the issue you are facing.

Thanks,

Ravi Chandra