Hello Babitha,

Stamitas Ntanos is correct in his explanation. To that, I would add the following:

1. Logistic regression (LR) does not require assumptions of normality.

2. LR can handle discrete or continuous independent variables.

3. Multiple linear regression (MLR) quantifies model accuracy via the standard error or variance error of estimate (or, for many people, the magnitude of the R-squared), whereas LR quantifies model accuracy via the (-2)LLR (lower is better) and the classification accuracy. While "pseudo-R-squared" statistics are often reported in LR software, it's not variance accounted for.

4. MLR solution is computed via a one-step equation (unless IVs have some linear dependency). LR uses an iterative, maximum-likelihood solution process to derive estimates of regression coefficients.

5. LR requires that you shift your thinking about a regression coefficient from "if X changes one unit, then Y is expected to change by B units, holding all other IVs constant," to "if X changes by one unit, then the log-odds of target category of Y being observed increases by B units (or, the odds of target category of Y increase by exp(B) units)."

Good luck with your work!

In logistic regression your dependent variable is ordinal or nominal (categorical) where in linear regression it is scale (numerical). Thus logistic regression can be ordinal logistic or multinomial logistic. Lastly if the dependent has only two categories the model is called binary logistic. I use such regression analysis in my article Article Public Perceptions and Willingness to Pay for Renewable Ener...

Hello Babitha,

Stamitas Ntanos is correct in his explanation. To that, I would add the following:

1. Logistic regression (LR) does not require assumptions of normality.

2. LR can handle discrete or continuous independent variables.

3. Multiple linear regression (MLR) quantifies model accuracy via the standard error or variance error of estimate (or, for many people, the magnitude of the R-squared), whereas LR quantifies model accuracy via the (-2)LLR (lower is better) and the classification accuracy. While "pseudo-R-squared" statistics are often reported in LR software, it's not variance accounted for.

4. MLR solution is computed via a one-step equation (unless IVs have some linear dependency). LR uses an iterative, maximum-likelihood solution process to derive estimates of regression coefficients.

5. LR requires that you shift your thinking about a regression coefficient from "if X changes one unit, then Y is expected to change by B units, holding all other IVs constant," to "if X changes by one unit, then the log-odds of target category of Y being observed increases by B units (or, the odds of target category of Y increase by exp(B) units)."

Good luck with your work!

You do not have to use it! as per your original question.

You may find these papers helpful:

https://statisticsbyjim.com/regression/choosing-regression-analysis/

https://maitra.public.iastate.edu/stat501/lectures/MultivariateRegression.pdf

Please Read carefully there is more info here than you asked about. Best, David Booth

thank you all

Babitha

Hi Babitha Ek,

All the responses here have been great. I particularly find the Jim Frost's article attached by David Eugene Booth as a good explanation. This explanation from stakeoverflow is also a good summary: https://stackoverflow.com/questions/12146914/what-is-the-difference-between-linear-regression-and-logistic-regression

Good luck!

Nadia H. Al-Noor

I am sorry but all your first three points are wrong, or at least problematic.

The logistic model is not not only used for binary outcomes as it is an important model for analyzing proportions (with a potentially varying denominator) that is closed ratios bounded by 0 and 1.

And the explanatory variables can be correlated, but not too much - same assumptions as OLS continuous regression. That is is why you have a logit model with several predictors.

And there is an underlying linear assumption but now on the logit scale. This assumption can be evaluated relaxed in Generalized Additive Models. Article “Moving Out of the Linear Rut: The Possibilities of Generali...

Article Generalized Additive Models, Graphical Diagnostics, and Logi...

The web source you point to is in error, or confused on all these three points. Much better to consult a good peer reviewed book from good publishers. Or a high end statistics training site from a reputable university, or a specialist software supplier for statistical analysis.

Hi, I would like to take this topic to continue the discussion about linear regression

In which cases I can use linear regression in a non-normal distribution?

I have been reading some validation studies which used linear regression even with a non-normal distribution. However, they did not justify why. Please, could someone explain it to me?

If the underlying probability of yes ( or indeed no) outcome lies between 0.2 and 0.8 , then a linear model would be fine; within this range the relationship between the logit and probability is essentially linear. My source is Sir David Cox when replying to questions at Nuffield College in the early 1990s.

https://www.jstor.org/stable/2983890?seq=1#page_scan_tab_contents

This post also represents an informed commentary on the issues involved

https://statisticalhorizons.com/linear-vs-logistic

Linear and Logistic regression are the most basic form of regression which is commonly used. The essential difference between these two is that Logistic regression is used when the dependent variable is binary in nature. In contrast, Linear regression is used when the dependent variable is continuous and nature of the regression line is linear. therefore it depends on your dependent variables you will going to use.

Israel Bekele Molla As per my earlier answer, logistic regression can also be used when the response is continuous, and is composed of a closed ratio where the numerator is some subset of the denominator. It is not just for binary outcomes. Indeed the binary is just a special case where the denominator is a 1 (the so-called number of trials) and the outcome can only be a 1 or 0.

Linear regression is used when the dependent variable is continuous and nature of the regression line is linear. In contrast, Logistic regression is used when the dependent variable is binary in nature.

Why do researchgate responders (e.g., Israel Bekele Molla and Hom Nath Chalise ) continue to give responses that Kelvyn Jones has already corrected? Maybe these responders (not Kelvyn) can explain.

Dear Babitha Ek

Linear regression needs a linear relationship between the dependent and independent variables. While logistic regression does not need a linear relationship between the dependent and independent variables.

Linear regression aims at finding the best-fitting straight line which is also called a regression line. Linear regression requires the dependent variable to be continuous i.e. numeric values (no categories or groups).While Binary logistic regression requires the dependent variable to be binary - two categories only (0/1). Multi-nominal or ordinary logistic regression can have dependent variable with more than two categories.

Linear regression is based on least square estimation which says regression coefficients should be chosen in such a way that it minimizes the sum of the squared distances of each observed response to its fitted value. While logistic regression is based on Maximum Likelihood Estimation which says coefficients should be chosen in such a way that it maximizes the Probability of Y given X (likelihood). With ML, the computer uses different "iterations" in which it tries different solutions until it gets the maximum likelihood estimates.

*Sample Size : Linear regression requires 5 cases per independent variable in the analysis.While logistic regression needs at least 10 events per independent variable

No apologies for being pedantic as it is important that researchers understand that the binomial logit model could be useful for analysis data such as percentages which are continuous ( as could Clog and probit models)

Neil Wrigley (1973) The Use of Percentages in Geographical Research Area Vol. 5, No. 3, pp. 183-186

https://www.jstor.org/stable/pdf/20000750.pdf?seq=1#page_scan_tab_contents

Moreover in the multinomial case, the same issue applies as you could have a set of proportions that sum to to 1 forming a closed ratio which usually produces an inbuilt negative correlation which has to be taking into account in the modelling.

A key feature of the logit (in both its Bernoulli and binomial form) is that the logit transformation is applied to the predicted response from previous iteration so that it is not the observed data that is transformed. To demonstrate this, take the 1 and 0 (out of 1) of the observed binary outcome and perform the logit transformation you will see that you get plus and minus infinity and you can go no further!

See my (longish) answer to this question:

https://www.researchgate.net/post/What_is_the_difference_between_binary_logistic_regression_and_binomial_logistic_regression

I am also deeply skeptical about rules such as 10 observations per variable as this does not take account of the possible collinearity between the predictors, nor does it take account of the potentially differing size of denominators . You need to do a proper power analysis.

See my answer to this question:

https://www.researchgate.net/post/When_can_a_researcher_relax_the_rule_of_ten_events_per_variable_in_Logistic_Regression

Finally on probits and ClogLog see

https://www.researchgate.net/post/Probit_and_logit_model2

https://techdifferences.com/difference-between-linear-and-logistic-regression.html

Just open the link you can get your answer.

Kaushik Kumar Panigrahi here we go again, this website is incorrect as I pointed out in earlier posts.

Logistic regression is used for assessing the effects of explanatory factors on the relative risk of outcomes. The logistic transformation can be interpreted as the logarithm of the odds of success vs failure.

You can read the book "Hosmer, D. & Lemeshow, S. Applied Logistic Regression. New York: John Wiley & Sons, Inc."

The following tutorials from UCLA will also help you

https://stats.idre.ucla.edu/stata/dae/logistic-regression/