Final answer:
To obtain the formula for the best least-squares fit to the data points (1,8), (2,2), (3,11), use the partial derivatives method.
Step-by-step explanation:
To obtain the formula for the best least-squares fit to the data points, we can use partial derivatives. Let's consider the given data points: (1,8), (2,2), (3,11).
Step 1: Define the general equation of the regression line as ŷ = a + bx, where a is the y-intercept and b is the slope.
Step 2: Take the derivative of the sum of squared differences between the observed y-values and predicted y-values with respect to 'a' and 'b.' Equate the derivatives to zero.
Step 3: Solve the system of equations to find the values of 'a' and 'b.'
Step 4: Substitute the obtained values of 'a' and 'b' into the general equation ŷ = a + bx to obtain the formula for the best least-squares fit.
Therefore, the formula for the best least-squares fit to the given data points is ŷ = -0.833x + 9.667.