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Unfortunately I have no help for the deep learning part, but I'll give a go on linear regression:
Linear regression is using one or more variables to predict a response. The way that it is predicted is with a line (hence the linear name). For example, if you wanted to predict how much food your dog ate, you could use linear regression. Let's say that the response is the total amount of food that your dog eats in a week, and the variable is how much the dog weighs. Knowing that a bigger dog should eat more, there will be a trend towards higher values as the dog weighs more. If you pooled 100 pet owners and asked the weight of their dog and how much the dog eats, you can put all of that data together and use a regression model to predict how much a dog of a specific weight might eat. The data can produce a line of best fit with modeling technology which basically makes the best line that minimizes the differences between the sample data and the predicted data (the line). You can also have more variables than one, such as the dog's eating habits (more or less meals a day), how much the dog exercises, or even the breed (which would be categorical, not numerical).

TL;DR: a linear regression model predicts one value based on another value and then fits a line to it that predicts the value as accurately as it can with the data given.

Let me see if I understand this. To piggy back off your example, the x axis can be the weight(lbs) of a dog from least to greatest and y axis can be the amount of food the dogs ate also in lbs and from least to greatest. Based on the data we plotted we draw a line that best fits the graph and that line can help estimate solutions? So if we have enough data and a customer comes with a X size dog asking how much their dog needs to eat, we can refer to the line and figure that out. Is this correct?

Yep, the line is just an estimation of what a dog of that size would probably eat based on the data with the X axis being weight and Y being the predicted food eaten. It would not be perfect because no dog is the same but it would be a pretty good guess with enough data.

Thank you thank you. I can see how this may apply in deep learning so ill continue to do research. The word regression is what confused me initially.

Regression is a somewhat cryptic name coined by a guy in the late 1800s. Basically it's referring to the fact if you have enough data, it will eventually head back towards the mean. You can probably google it to learn more because I'm not an authority figure lol.

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"Regression" is a math word that means "finding a line that best fits the data".

In your example, "Linear Regression", is just one type of regression that assumes the data wants to fit a straight line.

You hear about it a lot in algorithms because they are all about taking points of data, and trying to figure out what the larger scale process that's controlling the data.

Alternatively you might have something like "exponential regression", where the data wants to fit a curve. For example, if you wanted to chart the spread of COVID-19 in the early days of the pandemic, you'd want to use exponential regression. Linear regression would work at first, but once you started projecting out a week or two you'd see that your line stopped matching the actual infection rate suddenly, and then became very wrong, very quickly.

In practice, linear regression is much, much easier to both do and understand, so it's more "popular". Exponential regression usually requires computer analysis and is more confusing to lay-people. That's just why you hear about "linear regression" more commonly.