# Question: The method of least squares can be used to fit

The method of least squares can be used to fit curves to data. Using the method of least squares, find the normal equations that provide least squares estimates of a, β, and γ when fitting a quadratic curve of the form y = a + bx + γx2 to paired data.

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Making use of the fact that = y – β and β Sxy/Sxx , show that Use Theorem 4.15 show that Theorem 4.15 If X1, X2, . . . , Xn are random variables and Where a1, a2, . . . , an, b1, b2, . . . , bn are constants, then Use the formula for t of Exercise 14.28 to derive the following (1 – α) 100% confidence limits for β: In exercise If x01, x02, . . . , x0k are given values of x1, x2, . . . , xk and X0 is the column vector It can be shown that Is a value of a random variable having the t distribution with n- k- 1 degrees of freedom. (a) Show that for k ...Use the coding of Exercise 14.15 to rework both parts of Exercise 14.45. In exercise When the x’s are equally spaced, the calculation of and can be simplified by coding the x’s by assigning them the values . . . ,- ...Post your question