In econometrics, we know that in linear regression model, if you assume the error terms have 0 mean conditioning on the predictors and homoscedasticity and errors are uncorrelated with each other, then minimizing the sum of square error will give you a CONSISTENT estimator of your model parameters and by the Gauss- …

A line of best fit can be roughly determined using an eyeball method by drawing a straight line on a scatter plot so that the number of points above the line and below the line is about equal (and the line passes through as many points as possible).

To minimize the error with the line, we use gradient descent. The way to descend is to take the gradient of the error function with respect to the weights. This gradient is going to point to a direction where the gradient increases the most.

As you mention, the error are errors of prediction–the closer you are to the observed value with your regression equation, the smaller the error. Therefore, to reduce the error, you need to improve your prediction. To do so, you would add other predictors to your model that are related to your dependent variable.

As noted in the last chapter, the objective when estimating a linear model is to minimize the aggregate of the squared error….

1. First find the derivative; f′(x)=2x−4.
2. Set the derivative equal to 0 ; f′(x)=2x−4=0.
3. Solve for x ; x=2.
4. Substitute 2 for x into the function and solve for y.

Try to play with other input variables, and compare your RMSE values. The smaller the RMSE value, the better the model. Also, try to compare your RMSE values of both training and testing data. If they are almost similar, your model is good.

Regression analysis is sometimes called “least squares” analysis because the method of determining which line best “fits” the data is to minimize the sum of the squared residuals of a line put through the data.

Linear regression quantifies the relationship between one or more predictor variable(s) and one outcome variable. For example, it can be used to quantify the relative impacts of age, gender, and diet (the predictor variables) on height (the outcome variable).

Correlation quantifies the direction and strength of the relationship between two numeric variables, X and Y, and always lies between -1.0 and 1.0. Simple linear regression relates X to Y through an equation of the form Y = a + bX.

In regression analysis, there are usually two regression lines to show the average relationship between X and Y variables. It means that if there are two variables X and Y, then one line represents regression of Y upon x and the other shows the regression of x upon Y (Fig.

The first is a line of regression of y on x, which can be used to estimate y given x. The other is a line of regression of x on y, used to estimate x given y. If there is a perfect correlation between the data (in other words, if all the points lie on a straight line), then the two regression lines will be the same.

two lines

No limit. Must be positive. One positive and the other negative. Product of the regression coefficient must be numerically less than unity.

The regression line is sometimes called the “line of best fit” because it is the line that fits best when drawn through the points. It is a line that minimizes the distance of the actual scores from the predicted scores.

Linear regression consists of finding the best-fitting straight line through the points. The best-fitting line is called a regression line. The black diagonal line in Figure 2 is the regression line and consists of the predicted score on Y for each possible value of X.