Homework Help is Here – Start Your Trial Now!
Math
Statistics
3. Consider the assumptions of inference for regression. Do any of them seem to be violated? Explain.

3. Consider the assumptions of inference for regression. Do any of them seem to be violated? Explain.

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
See similar textbooks
icon
Related questions
Question
**Regression Assumptions Analysis** **3. Consider the assumptions of inference for regression. Do any of them seem to be violated? Explain.** __Graph Description:__ The image includes a scatter plot that illustrates the relationship between two variables, HP (horsepower) on the X-axis and Weight on the Y-axis. Along with the scatter plot, there is a fitted line (red line) which represents the regression line. - **X-axis (HP):** This axis ranges from 0 to 550 HP. - **Y-axis (Weight):** This axis ranges from 2000 to 7000 units (presumably pounds or kilograms). - **Data Points:** Blue dots scattered across the plot, indicating individual observations. - **Legend:** - Blue dots represent individual data points. - A red line represents the fitted regression line. __Analysis Considerations:__ 1. **Linearity:** The scatter plot seems to display a general upward trend, suggesting a positive linear relationship between HP and Weight. However, while many points roughly follow this trend, there is notable variance, particularly as HP increases. This needs careful consideration as potential non-linearity can violate regression assumptions. 2. **Homoscedasticity:** Homoscedasticity means that the variance of errors should be constant across all levels of the independent variable (HP). The scattering of dots around the fitted line appears to widen as HP increases, indicating possible heteroscedasticity. This could suggest a violation of this assumption. 3. **Independence of Errors:** The plot alone cannot verify the independence of errors between observations. Ensuring that data points are collected independently is necessary through the study design. 4. **Normality of Errors:** The scatter plot does not provide information on the distribution of residuals which must be normally distributed for valid inference. Additional diagnostic plots like a Q-Q plot of residuals are required to assess this assumption. **Conclusion:** The scatter plot suggests potential issues with homoscedasticity, indicated by an increasing spread of data points as HP increases. This could affect the reliability of the regression model. Whether or not the assumptions are violated ultimately requires further statistical tests and potentially improved data transformations or different modeling techniques to address these concerns.
Transcribed Image Text:**Regression Assumptions Analysis** **3. Consider the assumptions of inference for regression. Do any of them seem to be violated? Explain.** __Graph Description:__ The image includes a scatter plot that illustrates the relationship between two variables, HP (horsepower) on the X-axis and Weight on the Y-axis. Along with the scatter plot, there is a fitted line (red line) which represents the regression line. - **X-axis (HP):** This axis ranges from 0 to 550 HP. - **Y-axis (Weight):** This axis ranges from 2000 to 7000 units (presumably pounds or kilograms). - **Data Points:** Blue dots scattered across the plot, indicating individual observations. - **Legend:** - Blue dots represent individual data points. - A red line represents the fitted regression line. __Analysis Considerations:__ 1. **Linearity:** The scatter plot seems to display a general upward trend, suggesting a positive linear relationship between HP and Weight. However, while many points roughly follow this trend, there is notable variance, particularly as HP increases. This needs careful consideration as potential non-linearity can violate regression assumptions. 2. **Homoscedasticity:** Homoscedasticity means that the variance of errors should be constant across all levels of the independent variable (HP). The scattering of dots around the fitted line appears to widen as HP increases, indicating possible heteroscedasticity. This could suggest a violation of this assumption. 3. **Independence of Errors:** The plot alone cannot verify the independence of errors between observations. Ensuring that data points are collected independently is necessary through the study design. 4. **Normality of Errors:** The scatter plot does not provide information on the distribution of residuals which must be normally distributed for valid inference. Additional diagnostic plots like a Q-Q plot of residuals are required to assess this assumption. **Conclusion:** The scatter plot suggests potential issues with homoscedasticity, indicated by an increasing spread of data points as HP increases. This could affect the reliability of the regression model. Whether or not the assumptions are violated ultimately requires further statistical tests and potentially improved data transformations or different modeling techniques to address these concerns.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 3 steps

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Similar questions
Recommended textbooks for you
MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
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 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…
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
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
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman
SEE MORE TEXTBOOKS