# Question

We would like to fit the quadratic curve y = β1 + β2x + β3x2 to a set of points (x1, y1), (x2, y2), . . . , (xn, yn) by the method of least squares. To do this, let

(a) By setting the three first partial derivatives of h with respect to β1, β2, and β3 equal to 0, show that β1, β2, and β3 satisfy the following set of equations (called normal equations), all of which are sums going from 1 to n:

(b) For the data

Show that

a = −1.88, b = 9.86, and c = −0.995.

(c) Plot the points and the linear regression line for these data.

(d) Calculate and plot the residuals. Does linear regression seem to be appropriate?

(e) Show that the least squares quadratic regression line is 6y = −1.88 + 9.86x − 0.995x2.

(f) Plot the points and this least squares quadratic regression curve on the same graph.

(g) Plot the residuals for quadratic regression and compare this plot with that in part (d).

(a) By setting the three first partial derivatives of h with respect to β1, β2, and β3 equal to 0, show that β1, β2, and β3 satisfy the following set of equations (called normal equations), all of which are sums going from 1 to n:

(b) For the data

Show that

a = −1.88, b = 9.86, and c = −0.995.

(c) Plot the points and the linear regression line for these data.

(d) Calculate and plot the residuals. Does linear regression seem to be appropriate?

(e) Show that the least squares quadratic regression line is 6y = −1.88 + 9.86x − 0.995x2.

(f) Plot the points and this least squares quadratic regression curve on the same graph.

(g) Plot the residuals for quadratic regression and compare this plot with that in part (d).

## Answer to relevant Questions

Show that the endpoints for a 100(1 − γ)% confidence interval for α are For the data given in Exercise 6.5-4, with the usual assumptions, In Exercise 6.5-4 (a) Find a 95% confidence interval for μ(x) when x = 2, 3, and 4. (b) Find a 95% prediction interval for Y when x = 2, 3, and 4. To test whether a golf ball of brand A can be hit a greater distance off the tee than a golf ball of brand B, each of 17 golfers hit a ball of each brand, 8 hitting ball A before ball B and 9 hitting ball B before ball A. ...An ecology laboratory studied tree dispersion patterns for the sugar maple, whose seeds are dispersed by the wind, and the American beech, whose seeds are dispersed by mammals. In a plot of area 50 m by 50 m, they measured ...Let p be the fraction of engineers who do not understand certain basic statistical concepts. Unfortunately, in the past, this number has been high, about p = 0.73. A new program to improve the knowledge of statistical ...Post your question

0