(d) An ecologist uses this regression line to predict how many birds will join another colony when 95 percent of the adults from the previous year return. What is the prediction? Comment on the appropriateness of using the line in (b) for this prediction.(e) Calculate the correlation coefficient between X and Y. (Show details of your work.) **Understanding Sparrowhawk Colony Dynamics**One of nature's patterns connects the percent of adult birds in a colony that return from the previous year and the number of new adults that join the colony. Here are data for 10 colonies of sparrowhawks:| Percent return, X | 74 | 66 | 81 | 52 | 73 | 62 | 52 | 45 | 62 | 46 ||-------------------|----|----|----|----|----|----|----|----|----|----|| New adults, Y | 5 | 6 | 8 | 11 | 12 | 15 | 16 | 17 | 18 | 18 |**Explanation and Analysis:**This table presents two sets of data:1. **Percent return, X:** This row indicates the percentage of adult birds that returned to the colony from the previous year. The values range from 45% to 81% across the ten colonies.2. **New adults, Y:** This row shows the number of new adult birds that joined the colony. The values range from 5 to 18 new adults.The data suggest a potential relationship between the percentage of returning adults and the number of new adults that join the colony. As the percentage of returning adults decreases, the number of new adults seems to increase, hinting at a compensatory mechanism in sparrowhawk colonies. Further analysis could involve plotting these data points to explore the nature of this relationship visually, such as through a scatter plot, to determine if there is a correlation or other underlying pattern.

Given Information : One of nature's patterns connects the percent of adult birds in a colony that…

(d) An ecologist uses this regression line to predict how many birds will join another colony when 95 percent of the adults from the previous year return. What is the prediction? Comment on the appropriateness of using the line in (b) for this prediction. (e) Calculate the correlation coefficient between X and Y. (Show details of your work.)

(d) An ecologist uses this regression line to predict how many birds will join another colony when 95 percent of the adults from the previous year return. What is the prediction? Comment on the appropriateness of using the line in (b) for this prediction. (e) Calculate the correlation coefficient between X and Y. (Show details of your work.)

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Concept explainers

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.

Question

(d) An ecologist uses this regression line to predict how many birds will join another colony when 95 percent of the adults from the previous year return. What is the prediction? Comment on the appropriateness of using the line in (b) for this prediction.

(e) Calculate the correlation coefficient between X and Y. (Show details of your work.)

**Understanding Sparrowhawk Colony Dynamics**

One of nature's patterns connects the percent of adult birds in a colony that return from the previous year and the number of new adults that join the colony. Here are data for 10 colonies of sparrowhawks:

| Percent return, X | 74 | 66 | 81 | 52 | 73 | 62 | 52 | 45 | 62 | 46 |
|-------------------|----|----|----|----|----|----|----|----|----|----|
| New adults, Y | 5 | 6 | 8 | 11 | 12 | 15 | 16 | 17 | 18 | 18 |

**Explanation and Analysis:**

This table presents two sets of data:

1. **Percent return, X:** This row indicates the percentage of adult birds that returned to the colony from the previous year. The values range from 45% to 81% across the ten colonies.

2. **New adults, Y:** This row shows the number of new adult birds that joined the colony. The values range from 5 to 18 new adults.

The data suggest a potential relationship between the percentage of returning adults and the number of new adults that join the colony. As the percentage of returning adults decreases, the number of new adults seems to increase, hinting at a compensatory mechanism in sparrowhawk colonies. Further analysis could involve plotting these data points to explore the nature of this relationship visually, such as through a scatter plot, to determine if there is a correlation or other underlying pattern.

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