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We use "Derivative and sum of squared residuals" to derive the OLS betas.

Here's a step-by-step explanation:

1. OLS (Ordinary Least Squares) is a method used in linear regression to estimate the parameters of the regression line that minimizes the sum of the squared residuals.

2. Residuals are the difference between the observed and predicted values of the dependent variable.

3. To find the OLS betas (the parameters of the regression line), we first need to calculate the residuals for each observation in our data.

4. We then square these residuals and sum them up. This gives us the sum of squared residuals.

5. We want to find the betas that minimize this sum. To do this, we take the derivative of the sum of squared residuals with respect to each beta.

6. Setting these derivatives equal to zero gives us a system of equations. Solving this system gives us the OLS betas.

So, the correct answer is "Derivative and sum of squared residuals".