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Chapter 14

# Chapter 14 - Chapter 14 Describing Relationships...

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Chapter 14 Describing Relationships: Scatterplots and Correlation In this chapter Identifying correlation graphically Quantifying a linear correlation “Causal” research Identifying correlation graphically Correlation – an association or relationship between two variables Scatterplot or Scatter diagram – displays the relationship between two quantitative variables X axis – (independent variable or explanatory variable) Y axis – (dependent variable or response variable) The relationship is like in algebra when dealing with functions. In statistics, you must always decide which variable is X and Y based on which variable is dependent. The difference between what is done in algebra and in this class comes from the definition of a function; each X will have exactly one Y. That is not the case when dealing with data. Commonly you will give two individuals the same X and get different values for Y. Example Suppose you have two variables, dosage of drug and reduction in blood pressure. Which one should be your X and which one should by your Y? In this case reduction in blood pressure is the Y variable because the reduction in blood pressure would be dependent on the dosage of the drug. Therefore, the dosage of the drug is X, your independent variable. Below is some sample data for this situation. X = Dosage of Drug Y = Reduction in Blood Pressure 100 10 200 18 300 32 400 44 500 56 In order to graph this data, you simply plot the points on the xy-plane. Remember that we are looking for a relationship or pattern in the data. The graph for this data follows:

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Dosage of Drug and Reduction in Blood Pressure 500 400 300 200 100 60 50 40 30 20 10 X Y Notice in the above graph there is a pattern in the data. As the dosage of the drug increases, the reduction in blood pressure also increases. We will now look at the specific patterns you need to be able to identify. Perfect positive linear correlation – We will focus on linear patterns in this class. For the graph below, all the points are exactly on a line with a positive slope. We only say perfect if all the points are exactly on a given function. Positive is used because the line has a positive slope. It is important you use these exact terms.
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Chapter 14 - Chapter 14 Describing Relationships...

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