How can you analyze data relationships without regression or correlation?

Simple graphs for pairs of variables can be highly illuminating. Any hypothesis linking the pair could be even more helpful.

In scatter plots one can also show more than one dataset and find differences in distributions and correlation between variables!

This question is disturbingly mis- located, both philosophically and practically. The idea, or the notion, that a credible researcher would SUBSTITUTE (not yelling, just emphasizing) visualization techniques for correlation analysis, in the process of analyzing data, is risible. At the very least, correlation is a necessary (but admittedly not sufficient) COMPLEMENT to visualizing possible relationships. Failing to understand this is but another way for “data science”—i.e., IT and computer science-centric data science—to deny the salient role of statistical approaches for gaining insights into our shared reality. In so doing, it does a disservice to itself and its customers.

There are several ways you can do this such as through data visualization (all these scatter plots, heat maps) are visualizations. Visualizing data using bar/line charts, graphs, and plots like scatter can provide insights into relationships through identifying trends and patterns visually. The other one is ANOVA, which can help you compare means across multiple groups and identify if there are significant differences.

Another great use of scatter plots is to find non linear relationships. By looking at the plots we might be able to uncover quadratic, exponential or different relationships, which might hint ways to improve our models (a log tranformation, for instance).

A contingency table (also known as a cross-tabulation or crosstab) is a type of table in a matrix format that displays the (multivariate) frequency distribution of the variables. They're commonly used in survey research, data analysis, engineering, and scientific research. They provide a basic picture of the interrelation between two variables and can help find their interactions.

Contingency tables can be used for the creation of conditional probabilities, allowing us to furthermore fabricate conditional distributions. They are at the basis of Bayesian analysis.

Contingency table leads to chi-square which is a non-parametric equivalent of correlation and can be used when the data is categorical or when the data does not meet the required assumptions for correlation.

We can use contingency tables/ cross tabs. A contingency table can conceptualized as a table that shows the frequency or proportion of different categories or groups of two or more variables.

Contingency tables are relatively simple to create and interpret, making them accessible to both novice and experienced researchers.

Heatmaps are used to show relationships between two variables, one plotted on each axis. By observing how colors change across each axis, you can observe if there are any patterns in value for one or both variables. The variables plotted on each axis can be of any type, whether they take on categorical labels or numeric values. In the latter case, the numeric value must be binned like in a histogram in order to form the grid cells. Cell colorings can correspond to all manner of metrics, like a frequency count of points in each bin, or summary statistics like mean or median for a third variable. One way of thinking of constructing a heatmap is as a table or matrix, with color encoding on top of the cells.

Heatmaps are a great visualization tool that scale up very well up to very high numbers of variables (after all, per pair of variables one pixel is enough). Heatmaps can be very useful to detect patterns. There is a classic example of the incidence of measles in each state of the United States when, at some point the vaccine is introduced. After the vaccine introduction there is a significant drop on measles' cases, up until recent years when novax movements arose. A particular and very interesting use on heatmaps is clustering, where it's easier to see grouos of variables related to each other.

Heatmaps helps us to compare the data over different entities such as maps, calendar, webpages, more. We use heatmaps to encode the right linear color pattern to plot min and max with two color ranges starting with red and ending with lime color. This gives the plot a contrasting view to differentiate the magnitude of differences.

A specific technique for dimensionality reduction is principal component analysis. This technique works by looking at the "directions" where the variance is highest, and further looks for orthogonal directions. It has the benefit of greatly reducing dimensionality, but at the cost of having new axes that are not representative, because they were artificially fabricated. An example ks analyzing genomic expressions, going from several thousand genomic expressions to one hundred principal components, which allows for clustering and other modelling.

A very essential technique when we are handling data with more than 200 features. As we all are becoming more cautious about collecting data points we are also entering into the era of Curse of dimensionality. So to fight the battle of curses created by dimensionality, one such technique to master is Dimensionality reduction.

Common dimensionality reduction techniques include: PCA, LDA, t-SNE, UMAP, and more. They work in unique ways, but all share the goal of representing complex, high-dimensional data into a low-dimensional space (commonly a 2-D or 3-D space). This makes it possible to observe relationships and patterns in the original data, in a more intuitive way. They can also make for some very cool plots, which give a better understanding of our data structure. UMAP has the benefit of being a non-linear algorithm, while a linear technique like PCA may struggle to capture non-linear data relationships.

Graphs are very useful for the analysis of the spread of information. For instance, they can clearly show how people only follow and interact with people with similar interests in twitter. Using this graph, it's clear that in the U.S. there is a division between political parties and their supporters.

Regression is a general classification of machine learning algorithms commonly used for making predictions (ridge regression, lasso regression, KNN regression, etc.) Even the standard least squares regression is considered a machine learning technique.

Nowadays deep learning techniques that understand what are the hidden features of a datasets by themselves are the ones that should be learned to analyze unexplored datasets .

Machine learning models are highly applied forms of statistical models which are the old win in the new bottle. The only difference is the ability to work on large-scale data. If you want to predict a category then we go for classification models, if we want to predict a continuous variable we do with regression models, These two types of models are supervised models. If you don't have a target value to predict, but still want to understand the underlying patterns and relationship we go with clustering models. In very simple words. ML is not about predicting the future but understanding the hidden patterns in historical data. And remember history repeats.

These definitions are debateable: AI & ML. Linear regression is a method that relies on correlation, albeit multiple correlation that is able to control for all the variables in estimation. I agree that OLS is ML, but do not see ML as a branch of AI. Recall that with OLS we have to test for multicollinearity or high cross-correlation that occurs from variables that are in the estimation equation. It is not sufficient just to look at bivariate correlation to diagnose, one must use VIFS (Variance Inflation Factors) as well as condition indices to diagnose as multicollinearity biases confidence intervals. However, multicollear cases are still valid for prediction. Parameter estimates are unbiased, but the confidence intervals are biased.

Descriptive statistics: Look at measures like mean, median, and mode within groups to see if there are differences that suggest a relationship.

I do think that while descriptive statistics can help us view differences between groups, we could also check for how similar they are. If we have two groups with different means, we can superimpose their distribution plots. It can help us view the overlap, and to see if the mean difference is really that important, or if there are more observations with similar values in the the two groups.

Correlation vs Predictive Power Score : Correlation is a statistical method used to assess a possible linear association between two continuous variables.Therefore many non-linear relationships simply won’t be detected. For example, a sinus wave, a quadratic curve or a mysterious step function. Also, correlation is only defined for numeric columns. Predictive Power Score is an asymmetric, data-type-agnostic score that can detect linear or non-linear relationships between two columns. The score ranges from 0 (no predictive power) to 1 (perfect predictive power). It can be used as an alternative to the correlation.

Hi Bill, Wonderful and well-written paragraphs. You might consider adding agent-based modeling to your non-regression and non-correlation possibilities. Jerry

In market research, chi square test is very common used to suggest tow variables to be correlated, not necessary factor-result. But certain pattern of relationships could be identified initially. Then we can apply more advanced statistical analysis to investigate. Second t-test is also very common to suggest if there are significant difference of scores in two groups of respondents or samples.