Stat 226 - Section 2.3

# Stat 226 - Section 2.3 - Review Describing Relationships...

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Section 2.3 Least-Squares Regression Section 2.3 1 Review - Describing Relationships In sections 2.1 and 2.2 we added new exploratory data analysis tools. A scatterplot is a graph that shows the relationship between two quantitative variables. The correlation measures the direction and strength of a linear relationship between a pair of quantitative variables. Section 2.3 2 Regression Line Like a density curve for the distribution of a single variable, it would be useful to have a mathematical tool to describe the overall pattern of the relationship between two variables. The overall pattern could be described by drawing a straight line on the scatterplot. Section 2.3 3 Regression Line In statistics, the straight line description is especially useful when one variable can be used to explain or predict the other. This is the case when we have defined an explanatory variable and a response variable. A regression line is a straight line that describes how a response variable y changes as an explanatory variable x changes. Section 2.3 4 Use of Regression Line What can a regression line be used for? The regression line can often be used to predict the value of y for a given value of x . The overall pattern of the relationship can be described in terms of the characteristics of the regression line. We can can investigate further aspects once the regression line has been established, such as how observations deviate from the regression line. Section 2.3 5 Example - Toothpaste Sales A company that produces a particular brand of toothpaste is interested in predicting the demand (in millions of units sold) of its “whitening” toothpaste each month based on one or more variables. The company believes that one important predictor is the difference (in dollars) between its suggested price per tube and the industry average for similar products. In addition, the company has information on its advertising expenditures (in millions of dollars) each month. The company collects all of this information for a six-year period (72 months). What are the explanatory and response variables? Section 2.3 6

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Toothpaste Sales -0.1 0.0 0.1 0.2 0.3 6 8 10 12 Demand vs. Price Difference Price Difference (\$) Demand (Millions of Units) Section 2.3 7 Interpretation - Toothpaste -0.1 0.0 0.1 0.2 0.3 6 8 10 12 Demand vs. Price Difference Price Difference (\$) Demand (Millions of Units) What form does the relationship have?
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