2. Chapters 3 and 4.pptx

# 2. Chapters 3 and 4.pptx - Chapter 3 Scatterplots and...

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Chapter 3 Scatterplots and Correlation Chapter objectives : Explanatory and Response variables Scatterplots Interpreting scatterplots Adding categorical variables to scatterplots The correlation coefficient r 1

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Explanatory and Response Variables Response Variable (Dependent variable): Measures an outcome of the study, typically represented by Y. Captures the outcome of interest, defined from the purpose of the study. Explanatory Variable (Factor/ Independent variable): Used to explain/account for the variation in the values of the response variable. Typically represented by X. A more common type of factor is some kind of treatment : A specific experimental condition defined at multiple levels. 2
For example : For each of the following cases define the explanatory and response variable. 1. The typical amount of calories a person consumes per day and that person’s percent of body fat. 2. Inches of rain in the growing season and the yield of corn in bushels per acre. 3

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Displaying Relationships: Scatterplots (pg67) In the blood glucose data (from Chap 1 and 2) we were looking to see whether our response variable: fasting blood glucose level, differs across the two levels of the explanatory variable (in-class vs. individual instruction) i.e we are seeing whether a quantitative variable differs across the levels of a qualitative variable. A different method can be used when we want to compare whether two quantitative variables are related. 4
A common plot used to display the relationship between two quantitative variables is the Scatter plot . Example (e.x 3.7) The metabolic rate of a person is the rate at which the body consumes energy. Such a variable is important in studies of weight gain, dieting and exercise. In this study, data on the lean body mass and resting metabolic rate for 12 women and 7 men who are subjects in a study of dieting was examined. 5

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Lean body mass, given in kilograms, is a person’s weight leaving out all fat. Metabolic rate is measured in kilocalories (Cal) burned per 24 hours. Researchers believe that lean body mass has an important influence on metabolic rate. Part of the data is presented below: Subject Sex Mass (Kg) Rate (Cal) 1 M 62.0 1792 2 F 36.1 1666 18 M 51.9 1867 19 M 46.9 1439 1 M 62.0 1792 2 F 36.1 1666 18 M 51.9 1867 19 M 46.9 1439 6
To start lets take a look at a scatterplot between Lean body Mass and Metabolic rate. 7

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Do we observe any kind of trend (relationship) between Lean body mass and metabolic rate? What if we want to see whether this relationship differs by sex. 8
What do we notice? Female Male 9

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Interpreting Scatterplots After plotting two variables on a scatterplot, we describe the overall pattern of the relationship. Specifically, we look for … Form : linear, curved, clusters, no pattern.
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