How can we find regression between an independent variable and a dependent variable measured on nominal/ordinal scale?

Hi Suhail, It is a hard talk subject to be answered here in few lines and without charts to display, Let's try to break down the question into definitions first:
The two main variables in an experiment are the independent and dependent variable.

An independent variable is the variable that is changed or controlled in a project to test the effects on the dependent variable.

A dependent variable is the variable being tested and measured in a project.

The dependent variable is 'dependent' on the independent variable. As the experimenter changes the independent variable, the effect on the dependent variable is observed and recorded.

Nominal variables are used to “name,” or label a series of values. Ordinal scales provide good information about the order of choices, such as in a customer satisfaction survey.

The regression of variables can be identified and calculated using different methods :

you have used the word of "Regression" so I will assume that you are looking at Regression Analysis:

Simple Linear Regression
Simple linear regression is a technique that is appropriate to understand the association between one independent (or predictor) variable and one continuous dependent (or outcome) variable.
When there is a single continuous dependent variable and a single independent variable, the analysis is called a simple linear regression analysis . This analysis assumes that there is a linear association between the two variables. (If a different relationship is hypothesized, such as a curvilinear or exponential relationship, alternative regression analyses are performed.

So, in this case, your chart will have two axis X and Y

We could use simple linear regression analysis to estimate the equation of the line that best describes the association between the independent variable and the dependent variable. The simple linear regression equation is as follows:

Y'= B0 +B1X

where Y is the predicted or expected value of the outcome, X is the predictor, b0 is the estimated Y-intercept, and b1 is the estimated slope. The Y-intercept and slope are estimated from the sample data, and they are the values that minimize the sum of the squared differences between the observed and the predicted values of the outcome, i.e., the estimates minimize:
Total of (y-y") power 2

These differences between observed and predicted values of the outcome are called residuals. The estimates of the Y-intercept and slope minimize the sum of the squared residuals and are called the least squares estimates.

Residuals

Conceptually, if the values of X provided a perfect prediction of Y then the sum of the squared differences between observed and predicted values of Y would be 0. That would mean that variability in Y could be completely explained by differences in X. However, if the differences between observed and predicted values are not 0, then we are unable to entirely account for differences in Y based on X, then there are residual errors in the prediction. The residual error could result from inaccurate measurements of X or Y, or there could be other variables besides X that affect the value of Y.

Suhail -

Isn't this a case for multinomial logistic regression?

Kiron

Kevin, well done on briefing the regression, do you know it is my favorite indicator but it is different from what looks like on Kiron reference website