R Day #5 Tip of the Day - Linear Regression

I have taken up Udemy Data Science Classes. Below notes from Linear Regression Classes

Linear Regression 

• Analyze relationship between two or multiple variables
• Goal is preparing equation (Outcome y, Predictors x)
• Estimate value of dependent and independent variables using relationship equations
• Used for Continuous variables that have some correlation between them
• Goodness of fit test to validate model

Linear Equations

• Explains relationship between two variables
•  X (Independent- Predictor), Y (Dependent)
•  Y = AX + B
•  A (Slope) = (Y/X)
•  B - Intercept (Value of Y when X =0)
•  Equation becomes predictor of Y

Fitting Line

• Sum of squares of vertical distances minimal
• Best Line = least residual
• Difference between model and actual values are called as residuals

Goodness of Fit

• R square measure 
• Sum of squares of distances (Sum of squares of vertical distances minimal)
• Uses residual values
• Higher R square value better the fit (close to 1 higher fit)
• Higher Correlation means better fit (R square will also be high) 

Multiple Regression

• Multiple predictors involved (X Values)
• More than one independent variable used to predict dependent variable
• Y = A1X1 + A2X2 + A3X3 +ApXp + B

11 Important Model Evaluation Techniques Everyone Should Know

Homoscedasticity -  all random variables in the sequence or vector have the same finite variance

heteroscedasticity -  variability of a variable is unequal across the range of values of a second variable that predicts it

Pearson's correlation coefficient (r) is a measure of the strength of the association between the two variables

Happy Learning!!!