Curve Fitting Examples

Mathematical Modeling · Axiom Academy

EXAMPLE Curve Fitting Examples Fitting a linear model to experimental data using least squares Experimental Data: Spring Extension vs. Applied Force Goal: Find the best-fit linear model Identify the appropriate model form for this physical relationship Calculate the mean values needed for the least squares formulas Compute deviations from the mean for each data point Apply the least squares formula for the slope Calculate the y-intercept using the point on the regression line Write the final fitted model equation For a spring obeying Hooke's Law, what type of relationship exists between force and extension? Linear regression finds the best-fit line by minimizing the sum of squared residuals The slope formula is , measuring how y changes with x The y-intercept is found using The fitted spring constant tells us the spring extends about 2 cm per Newton of applied force Small intercept values (like -0.02 cm) can often be attributed to measurement uncertainty

This is the written version of the interactive lesson above. See the full Mathematical Modeling course.