Answered: What type of correlation exists between…

Math

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What type of correlation exists between the kilometers run per week and weight in kilograms?

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

The graph shown is titled "Weight vs. Exercise" and displays the weight of people who run every week, measured in kilograms on the vertical axis, against kilometers run per week on the horizontal axis.

### Graph Description:
- **Vertical Axis (Y-Axis):** Represents weight in kilograms, ranging from 83 kg to 90 kg.
- **Horizontal Axis (X-Axis):** Represents kilometers run per week, ranging from 0 to 6 kilometers.
- **Data Points:** A series of blue dots are plotted to show individual data points relating the weight of a person to the kilometers they run each week. The data appears to show variability rather than a clear trend or correlation.

### Question:
What type of correlation exists between the kilometers run per week and weight in kilograms?

#### Options:
A. Strong positive correlation
B. Weak positive correlation
C. Weak negative correlation
D. Strong positive correlation

(Note: There seems to be an error in the options as D repeats A.)

### Analysis:
- A positive correlation implies that as one variable increases, the other also increases.
- A negative correlation suggests that as one variable increases, the other decreases.
- Strong and weak describe the extent of the relationship, with strong indicating a clearer trend.

In analyzing the graph, the answer seems to aim at determining whether a meaningful relationship (strong or weak, positive or negative) can be inferred from the data presented.

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