# Notes 4a - Notes 4 BIVARIATE DATA Bivariate data is data...

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Notes 4 1 BIVARIATE DATA Bivariate data is data for which there are two variables for each observation . Example: The following bivariate data show the High school and college GPAs for 10 college sophmores. High School 3.3 4.0 2.9 3.5 3.8 3.7 3.7 2.8 3.2 3.6 College 3.5 3.9 3.3 3.6 3.9 3.8 3.4 3.0 3.2 3.8 Response/Dependent variable : measures the outcome of the study, i.e. the quantity that we are interested in. Explanatory/Independent variable : An explanatory variable is one that influences the values of the response variable, either directly or indirectly. As mentioned previously, we must always be wary of lurking variables and confounding. The “hidden” effect may cause us to misinterpret the relationship between the explanatory and response variables. Scatterplots A scatter plot displays any relationship between bivariate data in a graphical manner. Each point on a scatterplot marks a pair of observations taken from one individual in the sample. Typically, the independent variable (X) is plotted on the horizontal axis and the dependent variable (Y) is plotted on the vertical axis . Example: The table below gives the weights (in hundreds of pounds) and highway fuel usage rates (in miles per gallon) for a sample of new domestic cars. Weight 29 35 28 44 25 34 30 33 28 24 Fuel Usage 31 27 30 25 31 29 28 28 28 33 Which variable do you think is the response, Y? (Hint: Y depends on X)

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Notes 4 2 Fuel Usage vs Weight 24 25 26 27 28 29 30 31 32 33 34 23 25 27 29 31 33 35 37 39 41 43 45 Weight Fuel Usage Based on the data, can you expect to use more gas if you buy a heavier car? What might the fuel usage be for a car that weighs 40 hundred pounds? Interpreting scatterplots After plotting two variables on a scatterplot, we describe the relationship by examining the form , direction and strength of the association. We also look for an overall pattern and deviations
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Notes 4a - Notes 4 BIVARIATE DATA Bivariate data is data...

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