Linear regression is a linear model, a model that assumes a linear relationship between the input variables (x) and the single output variable (y). More specifically, that y can be calculated from a linear combination of the input variables (x). As an example we could use the equation to predict weight if we knew an individual's height. In this example, if an individual was 70 inches tall, we would predict his weight to be: Weight = 80 + 2 x (70) = 220 lbs. In this simple linear regression, we are examining the impact of one independent variable on the outcome. This model can be expressed as:
Y = mx + n
Where:
m = [N*∑Xᵢ*Yᵢ+∑Xᵢ*∑Yᵢ]/[N*∑Yᵢ-(∑Xᵢ)^2]
n = [∑Yᵢ-x*∑Xᵢ]/N
R = [∑(Xᵢ-ẋ)*(yᵢ-ŷ)]/[N*σₓ*σᵧ]
Also is a predictive analysis, linear regression analysis is used to predict the value of a variable based on the value of another variable. And the variable you want to predict is called the dependent variable. With this, we can make a grafic with Y = mass, and X = radius. So, we can extract the radius using this tipe of operations. Remember, that we can resolve this type of linear regression with Rstudio, using logarithmics equations.
Finally, we can see a grafic similar to the imatge made by R.
