Concept explainers
Recompute the regression fits from Probs. (a) 17.3 and (b) 17.17, using the matrix approach. Estimate the standard errors and develop 90% confidence intervals for the coefficients.
(a)
To calculate: The coefficient of the regression fit equation of the given databy the use of matrix approach and then calculate standard error and
x | 0 | 2 | 4 | 6 | 9 | 11 | 12 | 15 | 17 | 19 |
y | 5 | 6 | 7 | 6 | 9 | 8 | 7 | 10 | 12 | 12 |
Answer to Problem 22P
Solution:
The value of coefficient by the use of matrix approach is
Explanation of Solution
Given Information:
The data is,
x | 0 | 2 | 4 | 6 | 9 | 11 | 12 | 15 | 17 | 19 |
y | 5 | 6 | 7 | 6 | 9 | 8 | 7 | 10 | 12 | 12 |
Calculation:
The coefficient of the regression fit equation can be found out by the Matrix approach by following the below steps,
Step 1. First make Z matrix that contain column of ones in the first column and in the second column x value is shown.
Step 2. Now the coefficient of normal equation is made.
Step 3. Now compute the normal equation of the right hand side that is y data.
Step 4. The coefficient of the model can be found out by taking inverse of the result obtained in step 2 and step 3.
The following MATLAB will perform the desired steps,
On the command window, write this command as,
Now, the coefficient of normal equation is calculated as,
Now, the normal equation of y is calculated as,
Finally, the coefficient of the model can be found out,
Therefore, the value of coefficientis
Now, for calculating the standard error follow these commands,
Now calculate
The standard error of the given data is
Now for calculating
Then the standard error of each coefficient,
Thevalue of
Hence, the
(b)
To calculate: The coefficient of the regression fit cubic equation of the given databy the use of matrix approach and then calculate standard error and
x | 3 | 4 | 5 | 7 | 8 | 9 | 11 | 12 |
y | 1.6 | 3.6 | 4.4 | 3.4 | 2.2 | 2.8 | 3.8 | 4.6 |
Answer to Problem 22P
Solution:
The value of coefficient by the use of matrix approach is
Explanation of Solution
Given Information:
The data is,
x | 3 | 4 | 5 | 7 | 8 | 9 | 11 | 12 |
y | 1.6 | 3.6 | 4.4 | 3.4 | 2.2 | 2.8 | 3.8 | 4.6 |
Calculation:
The coefficient of the regression fit equation can be found out by the Matrix approach by following the below steps,
Step 1. First make Z matrix that contain column of ones in the first column and in the second column x value is shown.
Step 2. Now the coefficient of normal equation is made.
Step 3. Now compute the normal equation of the right hand side that is y data.
Step 4. The coefficient of the model can be found out by taking inverse of the result obtained in step 2 and step 3.
The following MATLAB will perform the desired steps,
On the command window, write this commandfor cubic equation as,
Now, the coefficient of normal equation is calculated as,
Now, the normal equation of y is calculated as,
Finally, the coefficient of the model can be found out,
Therefore, the value of coefficient is
Now, for calculating the standard error follow these commands,
The standard error of the given data is
Now for calculating
Then the standard error of each coefficient,
The value of
And,
Hence, the
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Chapter 17 Solutions
Numerical Methods For Engineers, 7 Ed
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