# The ultimate goal of the regression algorithm is to plot a best-fit line or a curve between the data

Regression analysis is a fundamental concept in the field of machine learning. It falls under supervised learning wherein the algorithm is trained with both input features and output labels. It helps in establishing a relationship among the variables by estimating how one variable affects the other.

Imagine you’re car shopping and have decided that gas mileage is a deciding factor in your decision to buy. If you wanted to predict the miles per gallon of some promising rides, how would you do it? Well, since you know the different features of the car (weight, horsepower, displacement, etc.) one possible method is regression. By plotting the average MPG of each car given its features you can then use regression techniques to find the relationship of the MPG and the input features. The regression function here could be represented as \$Y = f(X)\$, where Y would be the MPG and X would be the input features like the weight, displacement, horsepower, etc. The target function is \$f\$ and this curve helps us predict whether it’s beneficial to buy or not buy. This mechanism is called regression.

## Evaluating a Regression algorithm

Let’s say you’ve developed an algorithm which predicts next week’s temperature. The temperature to be predicted depends on different properties such as humidity, atmospheric pressure, air temperature and wind speed. But how accurate are your predictions? How good is your algorithm?

To evaluate your predictions, there are two important metrics to be considered: variance and bias.

## Variance

Variance is the amount by which the estimate of the target function changes if different training data were used. The target function \$f\$ establishes the relation between the input (properties) and the output variables (predicted temperature). When a different dataset is used the target function needs to remain stable with little variance because, for any given type of data, the model should be generic. In this case, the predicted temperature changes based on the variations in the training dataset. To avoid false predictions, we need to make sure the variance is low. For that reason, the model should be generalized to accept unseen features of temperature data and produce better predictions.

## Bias

Bias is the algorithm’s tendency to consistently learn the wrong thing by not taking into account all the information in the data. For the model to be accurate, bias needs to be low. If there are inconsistencies in the dataset like missing values, less number of data tuples or errors in the input data, the bias will be high and the predicted temperature will be wrong.

Accuracy and error are the two other important metrics. The error is the difference between the actual value and the predicted value estimated by the model. Accuracy is the fraction of predictions our model got right. […]

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