Correlation Practice

Front

What is correlation?

Back

Correlation is a statistical measure that describes the extent to which two variables change together. A positive correlation means that as one variable increases, the other also increases, while a negative correlation means that as one variable increases, the other decreases.

Front

What does a positive correlation indicate?

Back

A positive correlation indicates that as one variable increases, the other variable also increases. For example, the relationship between the number of hours studied and exam scores is often positively correlated.

Front

What does a negative correlation indicate?

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A negative correlation indicates that as one variable increases, the other variable decreases. For example, the relationship between the amount of time spent watching TV and grades in school may be negatively correlated.

Front

What is the correlation coefficient?

Back

The correlation coefficient is a numerical value that ranges from -1 to 1, indicating the strength and direction of a linear relationship between two variables. A value of 1 indicates a perfect positive correlation, -1 indicates a perfect negative correlation, and 0 indicates no correlation.

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What is an example of a positive correlation?

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An example of a positive correlation is the relationship between temperature and ice cream sales; as the temperature increases, ice cream sales tend to increase.

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What is an example of a negative correlation?

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An example of a negative correlation is the relationship between the amount of exercise and body weight; as exercise increases, body weight tends to decrease.

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What does it mean if there is no correlation between two variables?

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If there is no correlation between two variables, it means that changes in one variable do not predict changes in the other variable. For example, the number of hours spent playing video games and the amount of rainfall in a city are likely to have no correlation.

Front

What is a scatter plot?

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A scatter plot is a graphical representation of the relationship between two quantitative variables. Each point on the plot represents an observation, and the pattern of points can indicate the type of correlation.

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How can you determine the type of correlation from a scatter plot?

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You can determine the type of correlation from a scatter plot by observing the direction of the points. If the points trend upwards from left to right, it indicates a positive correlation. If they trend downwards, it indicates a negative correlation. If the points are scattered without any clear trend, there is no correlation.

Front

What is a transformation in the context of functions?

Back

A transformation in the context of functions refers to a change made to the function's graph, such as shifting it up or down, stretching it, or reflecting it. For example, h(x) = f(x) + 2 shifts the graph of f(x) up by 2 units.