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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.