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CHAPTER 15 Describing Relationships: Regression, Prediction, & Causation
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THOUGHT QUESTION Studies have shown a negative correlation between the amount of food consumed that is rich in beta carotene and the incidence of lung cancer in adults. Does this correlation provide evidence that beta carotene is a contributing factor in the prevention of lung cancer? Explain.
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THOUGHT QUESTION From past natural disasters, a strong positive correlation has been found between the amount of aid sent and the number of deaths. Would you interpret this to mean that sending more aid causes more people to die? Explain.
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LINEAR REGRESSION Objective: To quantify the linear relationship between an explanatory variable and a response variable. We can then predict the average response for all subjects with a given value of the explanatory variable.
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REGRESSION LINES If we notice that a scatterplot shows a straight- line relationship between two quantitative variables, we might want to summarize this overall pattern by drawing a line on the graph. A regression line is a straight line that describes how a response variable y changes as the explanatory variable x changes. A regression line is often used to predict the value of y for a given value of x .
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REGRESSION EQUATIONS When we have a scatterplot with a strong relationship, it’s relatively easy to draw a line close to the points. However, as we get more scatter on the scatterplot, this leads to the possibility of different people drawing different lines when basing it on eyesight alone.
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