11.10: Multiple Regression
Multiple regression assesses a linear relationship between one response or dependent variable and two or more independent variables. It has many practical applications.
Farmers can use multiple regression to determine the crop yield based on more than one factor, such as water availability, fertilizer, soil properties, etc. Here, the crop yield is the response or dependent variable as it depends on the other independent variables. The analysis requires the construction of a scatter plot followed by a multiple linear regression equation to calculate the multiple coefficient of determination, R2. Suppose the value of R2 is 96%; one can interpret that the different combinations of water and fertilizer explain 96% of the variation in the crop yield.
However, the value of R2 increases with the number of independent variables. So, an adjusted coefficient of determination that accounts for both - the sample size and number of variables is used during analysis.