Where a is the intercept and

b is the slope of the line calculated as in this formula.

And a is calculated as the mean upsilon minus b mean x.

It is possible to identify the confidence lenience of a regression line by creating

that zone or interval of confidence above and below the straight line.

To do this, we must calculate the residual variance,

we use this formula to calculate it.

Then, we can estimate the 95% confidence interval.

So, 95% of confidence interval, you just calculate by this equation.

We use upsilon plus or minus t multiplied by the interval

of confidence that we calculate from the residual variance last time.

Where in this case,

the formula is an upsilon that is a particular estimate arising from x.

Choose from this regression line, and

t is obtained from the tables for n minus 2 degree of freedom.

At P is 0.05 and n so is the total number of values of x and

upsilon, so n and x plus n upsilon.

Repeating the calculation for many values of upsilon arising from x,

it is possible to trace the confidence along the regression line.

When the points around the regression line are quite dispersed and the coefficient b

of the regression line is low, we need to verify the significance of the regression.

Which indicated the probability that there is a real linear relationship between

the variable x and the variables upsilon.

We use this formula of t.

If the calculated value of t, of the related degrees of freedom,

in this case n x upsilon minus 2 is greater than the value in the table,

the relationship between the two variables is significant.

In ecology, many related variables, may show convenient relationship.

In this case,

it is better to transform one of the two variables, usually with the logarithm, or

both, until the cartesian graph does not show a linear relationship.

Finally, it is important to clarify that the use of our regression analysis,

should be limited to cases in which you need to locate the line.

That ensure the best approximation of the point in the cloud and

while you request an estimate over variable in relation to the other.

When however, we want to measure the degree of our relationship between

two variables, the use of the correlation coefficient is more appropriate.

If the point are not dispersing symmetrically enough on both sides

of the regression line, for

all its length, it is recommended to don't use this type of analysis.

An analysis of residuals can be enlightening.

When we study, we want to compare the mean of our numbers of samples greater than two

we can use a procedure called ANOVA.

So the Analysis of Variants.

The Analysis of Variants assumes different names depending on how many

the dependent and independent variables are.

The one way ANOVA is used is when there is only one dependant variable, and

one independent variable.

The factorial ANOVA instead is used for

when we have only one dependant variable, and several independent variables.

The MANOVA, so the multivariate analysis of variance, is used when we have

more than one dependant variables, and several independent variables.

The ANOVA technique need can be extended to the analysis of written number factors.

The analyzed variable is always one in the ANOVA, but the number of factors or

classification criteria or

paths that distinguish the different samples is greater than one.

This is called a univariate multifactorial ANOVA.

There are many statistical software that carry out the calculation of the various

type of ANOVA in a few minutes by simply setting the data as required.

If we want to compare means of an ecological variable detected in

different samples, more than two, the analysis of variance with one criterion or

classification, one dependent variable and one independent is the best choice.

When instead we want to compare means of a ecological variable

detected in different samples, always more than two, but after some time.

The best technique is to analyze the variance with two classification criteria.

This is an ANOVA which estimates the effect of two independent variables

on a dependent variable.

Sex and season or weight, for instance.

Eye and temperature and diameter, and so soon.

So, guys this is the end of the statistical part applied to

study of biological diversity and also the end

of course biological diversity theories measure and data sampling technique.

I invite you to do module quiz and to check your knowledge with the final test.

I also invite you, if you need to acquire the certificate for

your professional life and your status.

Thanks for time you spent to follow this course and for your assignments.

It was a pleasure for me to be in touch with you in the former session.

I wish you all the best for your professional outstanding career.

We have an amazing biodiverse world yet to be discovered, good luck.