When I look at the movement, of the stock market, I get nervous !! thanks to the mathematicians who came up with great ideas to provide easy hacks to learn about stock speculation, and movement. If we really want to make decisions about the stock market, who is interested, the simple things you need to learn that basic knowledge about statistics, and the metrics of the error with the right information, which we will include in this content.

Before understanding, these concepts one has to be clear with important topic i.e“ Logistic Regression” which made me pick the knowledge from InsideAIML provided content for facile understanding.

          In R-squared coefficient is the determination of a statistical tool, which measures the level of safety of any operation, which may be due to the performance of a particular benchmark indicator.

R-squared (R2) is a statistical measure that represents the proportion of the variance for a dependent variable that's explained by an independent variable or variables in a regression model.  

Whereas correlation explains the strength of the relationship, between an independent and dependent variable, R-squared explains to what extent the variance of one variable, explains the variance of the second variable. So, if the R2 of a model is 0.50, then approximately half of the observed variation can be explained by the model’s inputs.

“Higher the “R-squared” the more variation is explained by our input variables so it is called the good model”.

  

     

Instead of working with multiple parameters, the easiest way to understand it is to check the accuracy of the model by looking at the R-squared, directly from the statistical description sheet from the generated project.

Let’s understand these points of R-squared, with the example of S&P portfolio performance.

The summary provides two R-squared values, namely Multiple R-squared, and Adjusted R-squared.

The Multiple R-squared is calculated as follows:

Multiple R-squared = 1 — SSE/SST

where:
1. SSE is the sum of square of residuals.

Residual is the difference between, the predicted value and the actual value, and can be accessed by prediction Models residuals.

It is calculated by summing the squares of difference between the actual value and the mean value.

For example,
let's say that we have different models with the value of 5, 6, 7, and 8, and a model predicts the outcomes as 4.5, 6.3, 7.2, and 7.9. Then,
SSE can be calculated as:

SSE = (5–4.5) ^ 2 + (6–6.3) ^ 2 + (7–7.2) ^ 2 + (8–7.9) ^ 2;
Here it calculates the difference between the original value with the predicted values where the output as:

0.04,

0.09,

0.04,

0.01.

SST can be calculated as:

mean = (5 + 6 + 7 + 8) / 4 = 6.5;

SST = (5–6.5) ^ 2 + (6–6.5) ^ 2 + (7–6.5) ^ 2 + (8–6.5) ^ 2.

0.25,

0.25,

0.25,

2.25. respectively

So these were basic concepts, of error metrics but let’s work with adjusted R-squared.

           The Adjusted R-squared value is similar to the Multiple R-squared value, but it accounts for the number of variables. This means that the Multiple R-squared will always increase.
when a new variable is added to the prediction model, but if the variable is a non-significant one, the Adjusted R-squared value will decrease.

Here,

        We begin understanding the concept of R-squared, and its characters. Then found, it keeps increases with increase in the variables, which is not a good sign for prediction of the movements, there comes the concept of Adjusted R-Square, which helped us giving the goodness of the model, also helped to penalize the values, with the additional variables which improve the existing models.

Hope this gave a clear understanding of R-Squared and Adjusted R-Squared, in this concept.

To know more about python programming language follow the insideaiml youtube channel.  

Happy Learning...

      

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