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9th Edition

Jay L. Devore

Publisher: Cengage Learning

ISBN: 9781305251809

Chapter 12.2, Problem 25E

Textbook Problem

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Show that *b*_{1} and *b*_{0} of expressions (12.2) and (12.3) satisfy the normal equations.

To determine

Show that

**Calculation:**

*Least squares estimate:*

In a linear equation *y*-intercept form and *x* is the independent variable and *y* is the independent variable.

The error function for the equation is,

*Normal equations of* *:*

The first normal equations of the error function will be obtained by finding the first derivative of

Hence, the first normal equation is

The second normal equations of the error function will be obtained by finding the first derivative of

Hence, the second normal equation is

In the linear equation the point estimates of the

Then the values of

*Slope:*

In a linear equation *y*-intercept form and *x* is the independent variable and *y* is the independent variable.

The general formula to obtain slope is,

*Y-intercept:*

In a linear equation *y*-intercept form and *x* is the independent variable and *y* is the independent variable.

The general formula to obtain *y-*intercept is,

Here, the objective is to prove that

*First normal equation:*

To prove that the value

The computation procedure goes as follows:

Thus, the first normal equation is satisfied by

Probability and Statistics for Engineering and the Sciences

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