Could anyone please explain why heat map represents the RELATIONSHIP AMONG VARIABLES?

Where did you get the idea that it does?

You’re plotting a dependent variable z which is a function of two independent variables x and y, so z=f(x,y).

To plot that on a flat piece of paper, one way is to say that the x-axis is horizontal and the y-axis is vertical, so every point on the piece of paper corresponds to a point (x,y). And associated with each point (x,y) is a value z=f(x,y).

Suppose we somehow converted those values of z into colours.

For example, we might say that z=0 was yellow and z=1 was blue, and values of x between 0 and 1 would be various shades of green.

At each point (x,y) on that heat map, you put the colour associated with that value of (x,y)

And to read the heat map, at each point you have a colour and you need to figure out the value associated with that colour

I have an example of heat map here, could you please explain the correlation between variables?

For example, when i see the SCATTER PLOT, i can identify the correlation between variables. However, when i see this heat map, i don’t have a clue about correlation between variables.

the only correlation I can immediately spot is that the 1st and 4th lines have very similar percentages in each of the 3 size categories.

To have correlation, the data need to be numerical. Furthermore, the scale must be at least cardinal.

Names of sectors aren’t numerical, and market cap bins are ordinal, but not cardinal.

The underlying data would be the distribution of firms by market cap for each of the various sectors.

If that underlying data was available, it would be possible to compare the distribution in the various sectors.

We only have a very coarse summary of the underlying data (the summary being the number of firms in each bucket (small, mid, large cap) for each sector.)

Taking data from his table,

1st row (communication services) small cap 14.29%, mid cap 29.25%, large cap 56.46%

4th row (health care) small cap 13.33%, mid cap 26.67%, large cap 60%

At least to me, that’s enough to indicate that there’s likely some sort of correlation between distribution of firms by market cap in the communication and health care sectors

Indicating . . . what, exactly?

If you divide cities/towns by size, then look at the percentage of small/medium/large cities/towns in California and Texas, they’ll probably be close to each other. So what?

This may be where the OP got some of his information

2023 Curriculum

CFA Program Level I

Quantitative Methods

Refresher Reading: Organizing, Visualizing, and Describing Data

A heat map is a type of graphic that organizes and summarizes data in a tabular format

and represents it using a color spectrum.

It is often used in displaying frequency distributions

or visualizing the degree of correlation among different variables.

To me, that would mean that the answer to the original question would be that it means you have a data set, you calculate correlations among the different variables in the data set, and you display those correlations in a heat map.

an excellent point.

In his heat map, there are 5 sectors, and the percentages appear to be close in only 2 of them (communications and healthcare).

In your example, if I looked at 5 states (say CA, TX, NY, PA, FL) and the percentage distribution of cities/towns by size was similar in CA and TX but completely different in the other 3 states, I’d be curious as to whether that was just happenstance or whether there was some reason for it