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Section 6.1: Scatterplots and Correlation (Day 1)

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Scatterplots A graph of points which show the relationship between two quantitative variables measured on the same individual (ex., the temperature outside vs. the amount of gas consumed to heat a house).

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Scatterplots The value for the x-axis is called the explanatory variable and is the independent variable for the data. The value for the y-axis is called the response variable and is the dependent variable for the data. This is an example of a scatterplot which is “negatively associated”.

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Scatterplots So, on the previous example, the temperature outside (explanatory variable) explains the amount of gas used to heat the house (response variable). The colder the temperature, the more gas used; the warmer the temperature, the less gas used. How could a similar situation be changed to a positive association?

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Scatterplots The explanatory variable here is IQ Test Score The response variable here is School GPA This is an example of a scatterplot with Positive Association A, B, and C could represent Outliers

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Describing Scatterplots Strength ◦ Strong—points follow a tight pattern. ◦ Weak—points are scattered widely. Form ◦ Straight-line (linear) ◦ Curved Direction ◦ Positively associated Both variables increase in value, or both variables decrease in value. ◦ Negatively associated One variable increases in value, while second variable decreases in value.

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Correlation Describes the direction and strength of a straight-line relationship between two quantitative variables. You cannot calculate correlation for curved graphs. Usually written as “r”. The range for correlation is -1 to +1 (remember your crossword puzzle ) A positive “r” denotes a positive association; a negative “r” denotes a negative association.

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Correlation The closer the number is to -1 or +1, the stronger the correlation. The closer the number is to 0, the weaker the correlation (or no correlation).

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Correlation Examples

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Homework Pages #3, 4, and 6

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