What is the test of significance for the coefficient of correlation. (Method 1 and Method 2). The second image is the guide. Thank you. I hope you can help me answer this.
What is the test of significance for the coefficient of correlation. (Method 1 and Method 2). The second image is the guide. Thank you. I hope you can help me answer this.
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
Concept explainers
Correlation
Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.
Linear Correlation
A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related.
Regression Analysis
Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.
Question
What is the test of significance for the coefficient of
Transcribed Image Text:INTERPRETATION OF COEFFICIENT OF CORRELATION
Strength of Correlation
Perfect positive correlation
Strong positive correlation
Moderately positive correlation
Weak positive correlation
Negligible positive correlation
Value of r
+1
+ 0.71 to + 0.99
+ 0.51 to + 0.70
+ 0.31 to + 0.50
+ 0.01 to + 0.30
No correlation
Negligible negative correlation
Weak negative correlation
Moderately negative correlation
Strong negative correlation
Perfect negative correlation
- 0.01 to - 0.30
- 0.31 to - 0.50
- 0.51 to - 0.70
- 0.71 to - 0.99
-1
b.) Does this degree of relationship is true for every year? (Use 0.05 level of significance)
TEST OF SIGNIFICANCE FOR THE COEFFICIENT OF CORRELATION (METHOD 1)
1. Formulation of Null and Alternative Hypotheses
Null Hypothesis
Ho: p = 0: There is no significant relationship between the total enrolment and the yearly profit
Alternative Hypothesis
Ha: p#0: There is a significant relationship between the total enrolment and the yearly profit
2. Select the level of significance
a = 0.05
3. Test Statistics
МЕТНOD 1
6.
; t-test ; two
tailed test
n =
TEST OF SIGNIFICANCE FOR THE COEFFICIENT OF CORRELATION (METHOD 1)
4. Define the Area of Rejection or the Critical Region
МЕТНOD 1:
dp: n-2
:1-1
-1 AU50
L. 8651
>
DECISION RULE:
Reject H, if the computed value is
a.) > 2.1657
b.)_< -1.9450
or
Otherwise, do not reject the Ho.
TEST OF SIGNIFICANCE FOR THE COEFFICIENT OF CORRELATION (METHOD 1)
5. Compute for the
-value:
n- 2
0.43 x
> 1.907105 999 8.911)
7. Interpretation:
Rejection
there is a significant relationship between the
total enrolment and the yearly profit
6. Decision:
of the null hypothesis (Ho) means that
Since, the computed _t_-value ( 3.9371 ) is
greater than the tabular value ( 2.3560 ).
Therefore,
reject the null hypothesis
(Ho) at 0.05_level of significance.
base on the sample of
9 years
using
0.05
from 2011 to 2019
tev
>
level of significance.
Mejact
TEST OF SIGNIFICANCE FOR THE
COEFFICIENT OF CORRELATION
METHOD 2
b.) Does this degree of relationship is true for every year? (Use 0.05 level of significance)
TEST OF SIGNIFICANCE FOR THE COEFFICIENT OF CORRELATION (METHOD 2)
1. Formulation of Null and Alternative Hypotheses
Null Hypothesis
Ho: p = 0: There is no significant relationship between the total enrolment and the yearly profit
Alternative Hypothesis
Ha: p#0: There is a significant relationship between the total enrolment and the yearly profit
2. Select the level of significance
a = 0.05
TEST OF SIGNIFICANCE FOR THE COEFFICIENT OF CORRELATION (METHOD 2)
3. Test Statistics
МЕТНOD 2
n = _9_ ; L-test (df : n-k)
Reject
Fail to reject
p= 0
Reject
p = 0
0.89
-1 = -0.6660
crifral whne
K = 0.6660
Critical wolue
1
r =
0.83
TEST OF SIGNIFICANCE FOR THE COEFFICIENT OF CORRELATION (METHOD 2)
4. Decision:
Since, the computed_-value (_
0.83
_) is _ greater than
the tabular
value ( 0.6660 ). Therefore,
_reject
the null hypothesis (Ho) at
_ 0.05 _ level of significance.
5. Interpretation:
Rejection
of
the
null
hypothesis
(Но)
means
that
there is a significant relationship between the total
enrolment and the yearly profit
9 years
from 2011 to 2019
base on the sample of
using
0.05
level of
significance.
Transcribed Image Text:It is expected that students who consistently perform
well in major tests, quizzes, assignments and seatworks
in the classroom also perform well in standardized
achievement test. A teacher decided to examine this
hypothesis. At the end of the academic year, she
randomly selected 10 students from her class. She
computes a correlation between the student's
achievement test scores and the overall GPA for each
student computed over the entire year. The data for the
10 students from her class are provided below.
Student Achievement
GPA
A
98
1.2
95
1.3
C
90
1.6
D
87
1.9
E
62
3.5
a. Compute the correlation coefficient.
F
85
2.0
b. Interpret the result in A.
c. Determine the regression equation.
G
76
2.9
H
88
1.5
d. If a student scored a 90 on the achievement test,
what would be his predicted GPA?
71
3.2
e. What could be a students' predicted GPA if he/she
scored 75 and 85?
92
1.4
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 3 steps with 9 images
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.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