Answer :
Final answer:
To simplify the formula for the standard error (s.e.) of b1, follow these steps: Maximize the function s(f) by minimizing the expression inside the square root, change the variable f to x = f², differentiate the function with respect to x, and substitute the optimal x value back into the equation.
Explanation:
To use the result of #79 to get a simpler formula for the standard error (s.e.) of b1, we can follow these steps:
- Observe that the function s(f) will be maximized when the expression inside the square root is minimized.
- Change the variable f to x = f².
- Differentiate the function with respect to x and set the derivative equal to zero to find the optimal value of x.
- Substitute the optimal x value back into the original equation and take its square root to find the optimal value of f.
By following these steps, we can derive a simpler formula for the s.e. of b1 than the one given on the AP formula sheet.
