CurveFit Studio

Linear Curve Fitting

Linear curve fitting, or simple linear regression, models the relationship between two variables by fitting a straight line through the data. It assumes the relationship follows:

y = mx + c

Here, $m$ is the slope of the line and $c$ is the y-intercept. The goal is to find the values of $m$ and $c$ that minimize the sum of the squared differences between the observed and predicted values.

Error Minimization

We use the method of least squares, minimizing:

S = \sum_{i=1}^n (y_i - (mx_i + c))^2

Taking derivatives of $S$ with respect to $m$ and $c$ , and setting them to zero yields:

m = \frac{n\sum x_i y_i - \sum x_i \sum y_i}{n\sum x_i^2 - (\sum x_i)^2}

c = \frac{\sum y_i - m\sum x_i}{n}

Once $m$ and $c$ are calculated, the fitted line $y = mx + c$ can be used to make predictions or interpret the relationship.