Assessment of Tea Bush Health and Yield Using Geospatial Techniques

Materials and Methods

1.2.11. Statistical Analysis
Correlation and regression were used for estimating the yield.
Correlation: It is the measure of strength of relationship between two variables. It is used to predict the value of one variable given the value of the other. Correlation is computed into what is known as the correlation coefficient, which ranges between -1 and +1. In probability theory and statistics, correlation, also called correlation coefficient, is a numeric measure of the strength of linear relationship between two random variables. The best known is the Pearson product-moment correlation coefficient, which is found by dividing the covariance of the two variables by the product of their standard deviations.

If we have a series of n measurements of X and Y written as x_i and y_i where i = 1, 2, ..., n, then the Pearson product-moment correlation coefficient can be used to estimate the correlation of X and Y . The Pearson coefficient is also known as the "sample correlation coefficient". It is especially important if X and Y are both normally distributed. The Pearson correlation coefficient is then the best estimate of the correlation of X and Y. The Pearson correlation coefficient is written:

where

and

are the sample means of x_i and y_i , s_x and s_y are the sample standard deviations of x_i and y_i and the sum is from i = 1 to n. As with the population correlation, we may rewrite this as

Regression

Linear regression is used to explain and/or predict. The general form is:

Y = a + bX + u

Where Y is the variable that we are trying to predict, X is the variable that we are using to predict Y, a is the intercept, b is the slope, and u is the regression residual.

In this study relationship between NDVI – LAI and the NDVI, ground LAI and MODIS LAI variability were developed to observe the variability and which in turn will help in yield prediction. A year wise correlation was developed between tea leaf yields and MODIS based NDVI of the tea estate during different months. Further tea leaf yield models were also developed to see the variability in the yield using the MODIS NDVI. The details were discussed in the results and discussion chapter.