Question

Suppose you were interested in crop yields and you had collected data on the amount of rainfall, the amount of fertilizer, the average temperature, and the number of sunny days.

How could you formalize this a as regression problem?

Answer 1

Multiple linear regression to forecast the crop yield
Multiple linear regression is a variant of “linear regression” analysis. This model is built to establish the relationship that exists between one dependent variable and two or more independent variables [19].For a given dataset where x1… xk are independent variables and Y is a dependent variable, the multiple linear regression fits the dataset to the model:

yi=β0+β1x1i+β2x2i+⋯+βkxki+εi
where β 0 is the y-intercept and β1,β2,…,βk parameters are called the partial coefficients. In matrix form

Y=XB+E
Y=⎡⎣⎢⎢⎢⎢⎢⎢⎢⎢⎢y1y2...yn⎤⎦⎥⎥⎥⎥⎥⎥⎥⎥⎥X=⎡⎣⎢⎢⎢⎢⎢⎢⎢⎢11.x11x21.x12x22.………x1kx2k...1..xn1..xn2………..xnk⎤⎦⎥⎥⎥⎥⎥⎥⎥⎥B=⎡⎣⎢⎢⎢⎢⎢⎢⎢⎢β0β1...βk⎤⎦⎥⎥⎥⎥⎥⎥⎥⎥E=⎡⎣⎢⎢⎢⎢⎢⎢⎢⎢ε0ε1...εn⎤⎦⎥⎥⎥⎥⎥⎥⎥⎥
Before applying the multiple linear regression to forecast the crop yield, it’s necessary to know the significant attributes from the database. All the attributes used in the database will not be significant or changing the value of these attributes will not affect anything on the dependent variables. Such attributes can be neglected. P value test is performed on the database to find the significant attributes and multiple linear regression is applied only on the significant values to forecast the crop yield.