A smaller residual error indicates a better fit. (d) To determine which regression is a better fit for the given data, we can compare the residual errors. The residual errors can be calculated by subtracting the actual y values from the predicted y values:įor the exponential regression, we can use the coefficients obtained from polyfit to evaluate the exponential function at the given x values: The polyval function evaluates a polynomial at specific values.įor the quadratic regression, we can use the coefficients obtained from polyfit to evaluate the polynomial at the given x values: (c) To calculate the residual errors for each method, we can use the polyval function in MATLAB. To find the best m and n, we need to exponentiate the first coefficient: The output p will be a vector of coefficients.

Now, we can use the polyfit function to fit a linear function to the transformed data: The exponential function can be written as y = me^(nx), which can be linearized by taking the natural logarithm of both sides: To find the best exponential function that fits the given data, we can use the polyfit function again, but this time we need to transform the data. The output p will be a vector of coefficients, where y = ax^2 + bx + c. Using the polyfit function, we can find the coefficients of the best second-order polynomial that fits the data: We want to fit a second-order polynomial, so n = 2. In this case, we have the following data: Where x and y are the vectors of x and y values, and n is the degree of the polynomial. The polyfit function fits a polynomial of a specified degree to a set of data points.

To find the best second-order polynomial that fits the given data, we can use the polyfit function in MATLAB.

Matlab polyfit