Calculate the standard errors of ˆα and βˆ.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
A) Calculate the standard errors of ˆα and βˆ.
B) Use a t-test to test H0 : β = 0 versus H1 : β < 0 with significance level 5%.
![We are interested in using the pH of the lake water (which is easy to measure) to predict the
average mercury level in fish from the lake, which is hard to measure. Let x be the pH of the
lake water and Y be the average mercury level in fish from the lake. A sample of n = 10 lakes
yielded the following data:
Observation (i)
1
3
4
5
6
8
10
pH (x;)
Average mercury level (y;) 0.15
8.2
8.4
7.0
7.2
7.3
6.4
9.1
5.8
7.6
8.1
0.04
0.40
0.50
0.27
0.81
0.04
0.83
0.05
0.19
Suppose we fit the data with the following regression model:
Y; = a + Bx;+ Ei, i =
1,..., 10,
where ɛi ~
· N(0, o²)
are independent. We have the following quantities: ī = E–1 Xi = 7.51,
n Li=1
vi=1
i=1
i=1
Some R output that may help.
> p1 <- c(0.01, 0.025, 0.05, 0.1, 0.9, 0.95, 0.975, 0.99)
> qt (p1, 8)
[1] -2.896 -2.306 -1.860 -1.397
1.397
1.860
2.306
2.896
> qt (p1, 9)
[1] -2.821 -2.262 -1.833 -1.383
1.383
1.833
2.262
2.821](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F84d7412a-0252-4765-a3f4-d04a4d856ec4%2F5fe69d2f-3bbf-4c96-8146-cd1a2e252e1b%2F1ujmvbo_processed.png&w=3840&q=75)
Transcribed Image Text:We are interested in using the pH of the lake water (which is easy to measure) to predict the
average mercury level in fish from the lake, which is hard to measure. Let x be the pH of the
lake water and Y be the average mercury level in fish from the lake. A sample of n = 10 lakes
yielded the following data:
Observation (i)
1
3
4
5
6
8
10
pH (x;)
Average mercury level (y;) 0.15
8.2
8.4
7.0
7.2
7.3
6.4
9.1
5.8
7.6
8.1
0.04
0.40
0.50
0.27
0.81
0.04
0.83
0.05
0.19
Suppose we fit the data with the following regression model:
Y; = a + Bx;+ Ei, i =
1,..., 10,
where ɛi ~
· N(0, o²)
are independent. We have the following quantities: ī = E–1 Xi = 7.51,
n Li=1
vi=1
i=1
i=1
Some R output that may help.
> p1 <- c(0.01, 0.025, 0.05, 0.1, 0.9, 0.95, 0.975, 0.99)
> qt (p1, 8)
[1] -2.896 -2.306 -1.860 -1.397
1.397
1.860
2.306
2.896
> qt (p1, 9)
[1] -2.821 -2.262 -1.833 -1.383
1.383
1.833
2.262
2.821
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps
Recommended textbooks for you
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman