An extensive study of a simple random sample (n = 400,000) of American elementary school students finds a very strong positive correlation (r - 0.9) between the number of hours a child sleeps per night and a childs grade on standardized exams. Based on this study, can we conclude that sleeping less causes students to perform poorly on exams? Explain.
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.
![**Study on Sleep and Academic Performance in Elementary School Students**
An extensive study of a simple random sample (n = 400,000) of American elementary school students finds a very strong positive correlation (r = 0.9) between the number of hours a child sleeps per night and a child's grade on standardized exams. Based on this study, can we conclude that sleeping less causes students to perform poorly on exams? Explain.
**Explanation:**
While the study indicates a very strong positive correlation (r = 0.9) between the number of hours slept and standardized exam grades, correlation does not imply causation. This means that although there is a strong relationship between sleep duration and exam performance, we cannot definitively say that sleeping less causes poor exam performance. Other factors may be involved, such as overall health, study habits, or socioeconomic status, which were not accounted for in the correlation. More controlled studies would be required to establish causation.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fddfcb673-5e58-4910-9aab-62d72cd94c11%2F539c2217-e67c-4d58-af19-35ae21f07152%2Fq05tj88_processed.png&w=3840&q=75)
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