Suppose that George wants to determine if the number of y insects in a given area is related to the number of flowers in that area. He creates three 1 m2 quadrats in his backyard and Data point 1 X¡ = 10 yi = 9 counts the number of flowers (x) and number of insects (y) Data point 2 X2 = 18 y2 = 16 Data point 3 in each quadrat. His data are shown in the table. Calculate the Pearson product-moment correlation X3 = 20 y3 = 14 Mean x = 16.00 y = 13.00 coefficient, r, using the formula Standard deviation sd= 5.292 sd,= 3.606 E zxi · Zyi r = п — 1 where z is the z-score for each value, x¡ represents the x-value for each data point, y; represents the y-value for each data point, and n represents the sample size. Complete the following five steps to calculate r, and give each of your answers precise to two decimal places. Step 1. Calculate the z-score for each x-value. X1 - x sdx x2 - x Хз — х Zx1 = Zx2 = Zx3 = sdx sdx

Q: Calculate the 4th derivative of the function y=x2/x−1 at x=2.

A:

Q: y = In( sech2x)

A: The objective of the question is to find the derivative of the function y = ln(sech^2(x)).

Q: у %3D V1+ 2х (1 — х)-3

A:

Q: Illustrate the standard error of z'?

A: Standard error (z-standard normal variable): The standard error of the mean is defined as the value…

Correlation

Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.

Linear Correlation

A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related. 

Regression Analysis

Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.