5. For page 18 of chapter 9 notes, an example asks for a confidence interval for the population slope B. What is the correct confidence interval for the slope ß? O (0.05137, 0.14702) (0.05629, 0.14814) (0.05429, 0.14514) O (0.05891, 0.14238)
5. For page 18 of chapter 9 notes, an example asks for a confidence interval for the population slope B. What is the correct confidence interval for the slope ß? O (0.05137, 0.14702) (0.05629, 0.14814) (0.05429, 0.14514) O (0.05891, 0.14238)
MATLAB: An Introduction with Applications
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ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
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Attached a picture of the notes in reference to the question, any help appreciated. Thanks.
![5. For page 18 of chapter 9 notes, an example asks for a confidence interval for the population
slope B. What is the correct confidence interval for the slope ß?
(0.05137, 0.14702)
(0.05629, 0.14814)
(0.05429, 0.14514)
(0.05891, 0.14238)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa09e37fb-885c-4c69-a39f-2c617567d0fd%2F3641295e-0b20-48ca-b684-7584e9b104c6%2Fgq1leht_processed.png&w=3840&q=75)
Transcribed Image Text:5. For page 18 of chapter 9 notes, an example asks for a confidence interval for the population
slope B. What is the correct confidence interval for the slope ß?
(0.05137, 0.14702)
(0.05629, 0.14814)
(0.05429, 0.14514)
(0.05891, 0.14238)
![The slope of the regression line.
The slope, b, of a regression line model, represents the slope of the sample on the graph.
Even the smallest error in the calculation of the slope can cause large errors in predictions.
Since the sample slope may be different by a small amount from the population slope, it is
important for us build a confidence interval for the population slope, ß, which is what the
model value of b tries to predict.
Example
Construct a 95% confidence interval for the slope ß for the house price data below.
Size (Sq. ft.)
2521 2555 2735 2846 3028 3049 3198 3198
Selling Price ($1000s) 400 426 428 435 469 475 488 455
Solution:
We enter the x-values (size) into L1 and the y-values (price) into L2.
Press STAT and highlight the TESTS menu and select LinRegTInt.
Enter L1 in the Xlist field and L2 in the Ylist field. Enter 0.95 in the C-Level field.
Select Calculate.
The confidence interval is (_
.).
This indicates that the expected population rate of change, ß, is between
The sample estimate rate of change which is b =
We interpret this confidence interval as the range of possible rates of change in selling price
per each additional square foot of house size.
and
The uncertainty with this population slope is due to confounding variables that affect price
other than house size, such as size of the lot, or the location of the neighborhood.
ADDITIONAL NOTE.
If the range of possible ß values contains zero, then = 0 is possible. When this occurs, it
means that the output (price) remains constant and is not affected by the input (size). This
is very bad result that means we cannot use house size to predict house price.
We always check the confidence interval to see if it contains zero. When this occurs,
we must write a sentence that explains that predictions cannot be made.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa09e37fb-885c-4c69-a39f-2c617567d0fd%2F3641295e-0b20-48ca-b684-7584e9b104c6%2Fr4cx7c_processed.png&w=3840&q=75)
Transcribed Image Text:The slope of the regression line.
The slope, b, of a regression line model, represents the slope of the sample on the graph.
Even the smallest error in the calculation of the slope can cause large errors in predictions.
Since the sample slope may be different by a small amount from the population slope, it is
important for us build a confidence interval for the population slope, ß, which is what the
model value of b tries to predict.
Example
Construct a 95% confidence interval for the slope ß for the house price data below.
Size (Sq. ft.)
2521 2555 2735 2846 3028 3049 3198 3198
Selling Price ($1000s) 400 426 428 435 469 475 488 455
Solution:
We enter the x-values (size) into L1 and the y-values (price) into L2.
Press STAT and highlight the TESTS menu and select LinRegTInt.
Enter L1 in the Xlist field and L2 in the Ylist field. Enter 0.95 in the C-Level field.
Select Calculate.
The confidence interval is (_
.).
This indicates that the expected population rate of change, ß, is between
The sample estimate rate of change which is b =
We interpret this confidence interval as the range of possible rates of change in selling price
per each additional square foot of house size.
and
The uncertainty with this population slope is due to confounding variables that affect price
other than house size, such as size of the lot, or the location of the neighborhood.
ADDITIONAL NOTE.
If the range of possible ß values contains zero, then = 0 is possible. When this occurs, it
means that the output (price) remains constant and is not affected by the input (size). This
is very bad result that means we cannot use house size to predict house price.
We always check the confidence interval to see if it contains zero. When this occurs,
we must write a sentence that explains that predictions cannot be made.
Expert Solution
![](/static/compass_v2/shared-icons/check-mark.png)
Step 1
Suppose be the size
And be the selling price
We have given the house price data as below,
Size | Selling Price |
2521 | 400 |
2555 | 426 |
2735 | 428 |
2846 | 435 |
3028 | 469 |
3049 | 475 |
3198 | 488 |
3198 | 455 |
Step by step
Solved in 3 steps with 1 images
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