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Agrochemistry

Statistical correlation and regression methods in agronomic research

For students

3 min read

AGROCHEMISTRY A

In practical agronomy, it is important to accurately determine how plant parameters are related to each other or to growing conditions. Pearson correlation allows for measuring this dependency and expressing it as a specific number. With this tool, one can forecast crop development and plan technological practices based on mathematical patterns.

  • Correlation coefficient range — from –1.00 to +1.00
  • Strong positive relationship — +1.00
  • Strong negative relationship — –1.00
  • No relationship — 0.00

A positive coefficient indicates a direct relationship between traits. As one parameter increases, the second one also increases accordingly. A negative value indicates an inverse relationship, where the growth of one indicator leads to a decrease in the other.

Assessing the strength of the relationship and regression calculations

To assess the tightness of the relationship in agronomic research, a generally accepted scale is used. It divides the strength of the dependency into three grades depending on the value of the linear correlation coefficient. This helps to quickly understand how significantly one factor affects another under field conditions.

Strength of the relationship between traits Correlation coefficient value (r)
Weak r < 0.3
Moderate r = 0.3–0.69
Strong r ≥ 0.7

The correlation coefficient does not depend on the scale of measurement. For example, the relationship between plant height and panicle length will be the same, regardless of whether you measure them in centimeters or inches.

The direction of the relationship determines the type of regression equation. In studies on the rice cultivar Krasnodarsky 424, the linear correlation between plant height and panicle length was r = –0.36. Depending on which trait is taken as the baseline (x or y), the mathematical model takes a different form:

  • basic regression equation: у = 28.029 + (-0.137377) · 1.2;
  • reciprocal regression equation (inverse dependency): у = 110.9 + 0.987179 · 3.2357.

To assess the reliability of the relationship, not only the correlation coefficient is taken into account, but also its statistical significance. Squaring the coefficient gives the coefficient of determination (r²), which reflects the proportion of total variability of the two traits. To check how close a curvilinear dependency is to a linear one, the F-criterion is calculated using the formula: F = ( (η² - r²) / (1 - η²) ) * (kx - 2). Here η² denotes the square of the correlation ratio of y on x, r² is the square of the linear correlation coefficient, n is the sample size, and kx is the number of groups in the x-series.

The relationship is recognized as linear only if the actual value of the F-criterion is less than the theoretical one (Ffact < Ftheor). In this experiment, the theoretical value Ftable is 3.18 (at a 5% significance level with 95% probability), and the relationship is confirmed as linear. If Ffact > Ftheor, then the correlation is non-linear, and a linear model cannot be used.

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