ANOVA and Linear Regression Resource

In summary, the conversation discussed resources for understanding ANOVA in linear regression. The speaker recommended getting "Minitab" and going through their exercises, which has a free trial version and costs $1600 for the full tool. They also suggested two books, "Applied Regression Analysis" by Norman Draper and Harry Smith, and "Applied Regression Analysis and Other Multivariable Methods" by David Kleinbaum and Lawrence Kupper, which focus on the connections between regression, ANOVA, and other statistical methods.
  • #1
Tosh5457
134
28
Hello,

Can someone please let me know of a resource (book or other) that explains how to use ANOVA in linear regression? I didn't even know what ANOVA was until some days ago so I'm looking for something that explains it thoroughly with deductions. The resources I've read focused solely on giving a formula on how to use the method, and no explanation on how to deduce the method... Thanks
 
Physics news on Phys.org
  • #2
If you're willing to go for the full Lean Six Sigma Black Belt training, you will escape knowing more about analysis of mean and many other statistical tools than you will likely ever need.
Short of that, I would suggest getting "Minitab" and go through their exercises:
https://support.minitab.com/en-us/m...ow-to/one-way-anova/before-you-start/example/

There is a free trial version - which may be sufficient for running the ANOVA exercises. Then the tool itself is about $1600.
http://www.minitab.com/en-us/products/minitab/pricing/
 
  • #3
A book that I liked was "Applied Regression Analysis" by Norman Draper and Harry Smith.

Another good one that concentrates on the connections between regression, ANOVA, and other statistical methods is "Applied Regression Analysis and Other Multivariable Methods" by David Kleinbaum and Lawrence Kupper.
 
Last edited:

1. What is ANOVA and how is it different from linear regression?

ANOVA (Analysis of Variance) is a statistical method used to compare the means of three or more groups. It is used to determine whether there is a significant difference between the means of these groups. On the other hand, linear regression is a statistical method used to model the relationship between a dependent variable and one or more independent variables. The main difference between ANOVA and linear regression is that ANOVA is used when the independent variable is categorical, while linear regression is used when the independent variable is continuous.

2. What are the assumptions of ANOVA and linear regression?

The assumptions for ANOVA include: normality of data, equal variances between groups, and independence of observations. Linear regression also assumes normality of data, linearity of the relationship between the dependent and independent variables, homoscedasticity (equal variance) of residuals, and independence of observations.

3. How do you interpret the results of an ANOVA or linear regression?

The results of ANOVA and linear regression are usually presented in the form of an F-test or t-test, respectively. These tests provide a p-value, which indicates the probability of obtaining the observed results by chance. A low p-value (usually less than 0.05) suggests that there is a significant difference or relationship. Additionally, the coefficients or effect sizes in linear regression can be interpreted to determine the strength and direction of the relationship between variables.

4. When should ANOVA or linear regression be used?

ANOVA should be used when there are three or more groups to compare, while linear regression should be used when there is a continuous dependent variable and one or more independent variables. ANOVA can also be used when there are multiple independent variables, but the categorical nature of the variables will limit the interpretation of the results to overall group differences.

5. Are ANOVA and linear regression appropriate for all types of data?

No, ANOVA and linear regression are not appropriate for all types of data. Both methods require certain assumptions to be met, such as normality and linearity, which may not be applicable to all datasets. In addition, both methods are best suited for analyzing quantitative data, and may not be appropriate for qualitative or categorical data.

Similar threads

I Exploring OLS and GLM Models: Understanding the Link Function and Coefficients
    • Set Theory, Logic, Probability, Statistics
Replies
3
Views
803
I Linear regression and probability distribution
    • Set Theory, Logic, Probability, Statistics
Replies
19
Views
2K
MHB Forecasting metric using regression. Is this a sound approach?
    • Set Theory, Logic, Probability, Statistics
Replies
3
Views
2K
How can I learn R for statistics software without prior knowledge?
    • Set Theory, Logic, Probability, Statistics
Replies
5
Views
3K
A Error in (Multi)linear Regression
    • Linear and Abstract Algebra
Replies
3
Views
1K
I Least squares line - understanding formulas
    • Set Theory, Logic, Probability, Statistics
Replies
5
Views
1K
Bivariate regression, dummy variables and r^2
    • Set Theory, Logic, Probability, Statistics
Replies
1
Views
2K
Regression Analysis: Finding Optimal Parameters for Non-Linear Functions
    • Set Theory, Logic, Probability, Statistics
Replies
2
Views
2K
What would be a good book for learning Linear Algebra by myself?
    • Science and Math Textbooks
Replies
12
Views
3K
MHB Linear Regression Gradient Descent: Feature Normalization/Scaling for Prediction
    • Set Theory, Logic, Probability, Statistics
Replies
2
Views
3K

Hot Threads

Recent Insights

Back
Top