Chapter 6 - Chapter 6 Correlation and Linear Regression How...

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Chapter 6: Correlation and Linear Regression How can we determine if 2 quantitative variables are related to each other? If there is a linear association, how can that information help understand and describe the data? Suppose we want to predict the assessed value of a house in a particular community. We could select a single random sample of size n houses from the community, 186
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estimate μ , and then use this quantity to predict the house’s assessed value. A better method uses information that is available to any property appraiser – square feet of floor space and age of the house. If we measure square footage and age at the same time as assessed value, we can establish a relationship that lets us use these variables for prediction. MSIT 3000 Section 6.1: Looking at Scatterplots Scatterplot Graphical display to determine pattern of association of two quantitative variables: 187
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Explanatory variable , x, (input), explains or influences changes in a response variable, horizontal axis Response variable , y, (output), measures an outcome of a study, vertical axis Internet Usage and Gross National Product (GDP) 188
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Examining a Scatterplot 1. Are the two variables both quantitative? 2. Is linear regression appropriate for the data being investigated? 3. Are there any outliers? 189
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In any graph of data, look for the overall pattern and for striking deviations from that pattern. You can describe the overall the shape and direction of the relationship pattern by graphing a scatterplot. An important kind of deviation is an outlier, an individual value that falls outside the overall pattern of the relationship. Positive relationship – an increase in x is associated with an average, or typical increase in the response variable. negative relationship – the response variable has a tendency to decrease as the explanatory variable increases. Ex: Would you expect a positive association, a negative association or no association between the age of the car and the mileage on the odometer? 190
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Positive association Negative association No association None of the above Ex: Would you expect a positive association, a negative association or no association between the age of a full-time college student and gender? Positive association Negative association No association None of the above Ex: The speed of a car and the distance required to come to a complete stop. Positive association Negative association No association Ex: The degree of job satisfaction and the number of absences from work. (Scale 1-7 where 7 is “Extremely Satisfied”) 191
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Positive association Negative association No association Ex: The size (carat) of a diamond and the cost. Positive association Negative association No association Ex: Which of the following conditions does NOT need to be checked when using correlation?
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