Statistical Analysis

Statistical Analysis

Introduction

Regression is a method of data analysis of the economic reality that serves to highlight the relationships between different variables. The regression also allows us to determine the dependence of the series of X and Y values, predicting the value and estimate that would be obtained for a value x that is not in the distribution. The linear regression analysis is a statistical technique used to study the relationship between variables. Simple linear regression statistical method is used to measure the relationship between two variables. In linear regression, one variables is dependent variable) and the other is independent variable or interpreter, which is causing the change in the dependent variable. Linear regression is called when the function is linear, i.e., requires the determination of two parameters: the slope and intercept of the regression line, y = ax + b.

In a simple regression analysis there is a response or dependent variable (y) may be the number of species abundance or presence-absence of a single species and explanatory or independent variable (x). The purpose is to obtain a simple function of the independent variable, which is able to describe as closely as possible the variation of the dependent variable. As the observed values ??of the dependent variable generally differ from those predicted by the function, it has an error. The most effective role is one that describes the dependent variable with the least possible error or, in other words, with the smallest difference between observed and predicted values.

The difference between observed and predicted values ??(the error function) is called residual variation or debris. To estimate the parameters of the function using the least squares fit. However, with this type of strategy is necessary that the waste or errors are normally distributed and to vary similarly over the entire range of values ??of the dependent variable. These assumptions can be tested by examining the distribution of waste and its relationship with the dependent variable.

When the dependent variable is quantitative (e.g., the number of species) and the relationship between two variables is a straight line function of type y = c + bx, where c is the intercept or the cutoff value of the regression line with the axis of the dependent variable (a measure of the number of species present when the environmental variable has its minimum value) and b is the slope or regression coefficient (the rate of increase in the number of species per unit of environmental variables considered).

The simplest polynomial function is the quadratic (y = c + bx + bx2) that describes a parabola, but you can use a cubic function of an order or other even more capable of achieving a nearly perfect fit to the data. When the dependent variable is expressed in qualitative data (presence-absence of a species) we recommend using logistic regression analysis (y = [exp (c+bx)] / [1+exp (bx+c)]).

Discussion

The data set for this regression analysis is generated randomly; the observations in a table are given ...