**Interpreting the Correlation Matrix**Refer to the relevant pages in your textbook for a detailed understanding of the strength of relationships between the variables (pages 86-87 for strength, page 77 for type of correlation). Consider whether a relationship is weak, moderate, or strong, and if it is positive (direct) or negative (indirect). **Understanding the Matrix:**- **Body Weight in kg vs. Total Sleep (hours/day):** Correlation of -0.307 indicates a weak negative relationship. This implies that as body weight increases, total sleep tends to decrease slightly.- **Body Weight in kg vs. Sleep Exposure Index (1-5):** Correlation of 0.338 suggests a weak positive relationship, indicating that higher body weight is associated with a slightly higher sleep exposure index.- **Body Weight in kg vs. Maximum Life Span (years):** Correlation of 0.302 points to a weak positive relationship, suggesting an association where increased body weight could relate to a slightly longer life span.- **Total Sleep (hours/day) vs. Sleep Exposure Index (1-5):** Strong negative correlation of -0.642 implies that more sleep hours are associated with a lower sleep exposure index.- **Total Sleep (hours/day) vs. Maximum Life Span (years):** Moderate negative correlation of -0.410 means that more sleep is somewhat associated with a shorter maximum life span.- **Sleep Exposure Index (1-5) vs. Maximum Life Span (years):** Correlation of 0.360 indicates a weak positive relationship, suggesting that a higher sleep exposure index might be associated with a slightly longer life span.**Provide an Interpretation:**Utilize this matrix to consider each variable’s relationship and its implications in broader studies or practical applications. Reflect on any possible causations, limitations of the correlations, and possible external factors influencing these relationships.

The given Correlation matrix is:

Answered: Interpret the correlation matrix below.…

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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Below is a correlation matrix for variables related to the annual salary for 30 employees at a company. The variables are gender (1 for female; 0 for male), age, number of years of relevant work experience prior to employment at the company, number of years of employment at the company, the number of years of post-secondary (college) education, and annual salary. Which variable has the strongest linear relationship with salary? Which two variables have the weakest linear relationship? Interpret the negative correlation between gender and salary
Professor Rene conducts an experiment and determines that variables A and B have a correlation. Based on this correlation, he claims that A is the cause of B. Is this statement correct? Explain.
Data from a certain city shows that individuals with more pets tend to have lower blood pressure (BP). From this information alone, we can say that pet ownership and BP are negatively (inversely) correlated. This may or may not be a causal relationship. pet ownership and BP are not related. pet ownership causes BP to be lower. pet ownership and BP are positively related. This may or may not be a causal relationship. 000
You might expect the correlation between the horsepower of new cars and their gas mileages in miles per gallon to be: Group of answer choices A substantial negative correlation A substantial positive correlation A small correlation
Susan, a personal trainer, was interested in whether or not there was a linear relationship between the number of visits her clients made to the gym each week and the average amount of time her clients exercised per visit. She took the following data. Client 1 2 3 4 5 6 Number of visits per week 1 3 4 2 3 5 Average time spent exercising per visit (hours) 2 1.5 1 2 2 0.30 If the correlation coefficient is –1, which answer is correct? Group of answer choices The slope of the best fit line is positive. The data fit exactly on a line with negative slope. The slope of the best fit line is –1. The data fit exactly on a line with positive slope.
A statement is made about correlation. State whether the correlation is positive or negative and whether the correlation is most likely due to coincidence, a common underlying cause, or a direct cause. If there is an underlying cause, state what the underlying cause is. If one directly causes the other, state which is the cause and which is the effect.(a) In Angela's class, the taller students got lower scores on the test.(b) As Thomas's income rose over the last 20 years so has his stress level.
How can you interpret a correlation value of .885? Moderate, Negative, Direct No Relationship Moderate, Positive, Inverse Strong, Positive, Direct
For a data set of weights (pounds) and highway fuel consumption amounts (mpg) of twelve types of automobile, the linear correlation coefficient is found and the P-value is 0.009. Write a statement that interprets the P-value and includes a conclusion about linear correlation.
C. Give an example for each of the following: a. Two variables in which you have enough reasons to explain their cause-and-effect relationship. State the independent (x) and dependent variable (y). Provide also description of the cause-and-effect relationship. b. Two variables from which a considerable possible nature of linear correlation may exist. Explain briefly the possible nature of the relationship. State both variables and give a short description of their relationship.
A phrase often repeated in this class is "correlation is not causation". Which of the following best describes what this phrase means? Correlation is not causation means that just because two values appear to be related on a graph doesn't mean that one necessarily causes the other. Correlation is not causation means that when we see values that move together (e.g. ice cream sales and murder rates), we can assume that one must be causing the other. Correlation is not causation means that if values move in opposite directions (e.g. average temperature goes down and grades go up), we can assume that one must influence to the other. O Correlation is not causation means that when values are shown to be related in a graph, this is proof that they are not causal.
Which of the following statements about correlation is true? Question content area bottom Part 1 Choose the correct answer below. A. We say that there is a positive correlation between x and y if there is no distinct pattern in the scatterplot. B. We say that there is a positive correlation between x and y if the x-values increase as the corresponding y-values decrease. C. We say that there is a positive correlation between x and y if the x-values increase as the corresponding y-values increase. D. We say that there is a negative correlation between x and y if the x-values increase as the corresponding y-values increase

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