stats ch 12

# stats ch 12 - Chapter 3/11 Exploring Association between...

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Chapter 3/11 : Exploring Association between two Quantitative variables . In Statistics we have to deal with many variables and some of them may be related to each other in some way. The most common form of relation (or association) between two variables is that of “cause- and-effect” i.e one variable may be causing a change in another variable or vice versa. Example : Suppose there are 25 cars in a used-car dealership lot in your area. For each car the owner (of the lot) has information on its weight and mileage (number of miles it travels on a gallon of gas). Obviously, weight and mileage are quite related since heavier the car, lesser should be its mileage. All the above variables are quantitative since they take numerical values. In this Chapter we will learn how to analyze association between two quantitative variables. For this purpose we have to be familiar with the following two terms : Response variable (Y) : It is the outcome variable i.e it measures the outcome of a process.

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Explanatory variable (X) : It is the causal variable i.e the variable which causes the outcome as we see it. Eg : For the above example, the mileage of a car is a response variable and its weight is an explanatory variable because it is the weight of a car which determines how much gas it will consume. To get a quick but modest idea of the relationship between two quantitative variables, we should first plot the response variable (Y) against the explanatory one (X) in what is called a scatterplot . Here the values of X and Y for a subject is represented by a point. A scatterplot tells us : Whether X and Y are positively associated (depicted by a upward trend in the points). Or whether X and Y are negatively associated (depicted by a downward trend in the points). Whether the trend (in the points) can be reasonably approximated by a straight line. Whether there are any unusual points which falls well apart from the general trend of the points.
Eg : The scatter plot of mileage (Y) against weight (X) of the 25 cars is as follows : WEIGHT 7000 6000 5000 4000 3000 2000 MILEAGE 40 30 20 10 Observations : The points show a strong downward trend i.e mileage and weight have a negative association. So, heavier cars tend to have poorer gas mileage.

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We can approximate the above trend by a straight line reasonably well. We donot see any point which falls well apart from the general trend of the points. i.e there doesnot seem to be any unusual observations. If the datapoints in a scatter plot have a straight line
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## This note was uploaded on 10/19/2009 for the course STA 3024 taught by Professor Ta during the Spring '08 term at University of Florida.

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stats ch 12 - Chapter 3/11 Exploring Association between...

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