R2 – (k + 1) F-ratio 1 R2 k 40, k = 5, and R? = 0.20. Calculate the F-ratio. d. Suppose that n = Perform the usual test of model adequacy to determine whether the five explanatory variables jointly and significantly affect the response variable.
R2 – (k + 1) F-ratio 1 R2 k 40, k = 5, and R? = 0.20. Calculate the F-ratio. d. Suppose that n = Perform the usual test of model adequacy to determine whether the five explanatory variables jointly and significantly affect the response variable.
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
![**Transcription for Educational Website**
**F-ratio Calculation and Model Adequacy Test**
**Formula:**
\[ F\text{-ratio} = \frac{R^2}{1 - R^2} \cdot \frac{n - (k + 1)}{k} \]
**Problem:**
d. Suppose that \( n = 40 \), \( k = 5 \), and \( R^2 = 0.20 \). Calculate the \( F\)-ratio. Perform the usual test of model adequacy to determine whether the five explanatory variables jointly and significantly affect the response variable.
**Explanation:**
- **\( R^2 \):** Coefficient of determination representing the proportion of variance explained by the model.
- **\( n \):** Total number of observations or data points.
- **\( k \):** Number of explanatory (independent) variables.
This formula allows us to test whether the set of explanatory variables in a multiple regression model significantly contributes to predicting the response variable. The higher the \( F\)-ratio, the more significant the contribution of the explanatory variables.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa89dc4a0-3781-41ca-831d-61fcc7d61ff9%2Fb4390d4a-ef9c-432f-bbe5-387de47f93a4%2Ftihox5v_processed.png&w=3840&q=75)
Transcribed Image Text:**Transcription for Educational Website**
**F-ratio Calculation and Model Adequacy Test**
**Formula:**
\[ F\text{-ratio} = \frac{R^2}{1 - R^2} \cdot \frac{n - (k + 1)}{k} \]
**Problem:**
d. Suppose that \( n = 40 \), \( k = 5 \), and \( R^2 = 0.20 \). Calculate the \( F\)-ratio. Perform the usual test of model adequacy to determine whether the five explanatory variables jointly and significantly affect the response variable.
**Explanation:**
- **\( R^2 \):** Coefficient of determination representing the proportion of variance explained by the model.
- **\( n \):** Total number of observations or data points.
- **\( k \):** Number of explanatory (independent) variables.
This formula allows us to test whether the set of explanatory variables in a multiple regression model significantly contributes to predicting the response variable. The higher the \( F\)-ratio, the more significant the contribution of the explanatory variables.
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 2 steps with 2 images
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