Chapter7-9 - Chapter 7 (Scatterplots, Association,...

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1 Chapter 7 (Scatterplots, Association, Correlation) In chapters 7-9 we will be considering relationships/associations between two quantitative variables measured on the same set of individuals. Similar to 1-variable data, we should begin by graphing the data and then look for overall patterns or deviations in the data. Scatterplots are used to plot 2-variable data. Both variables must be quantitative variables (can be measured numerically) A scatterplot is simply a plotting of data points with one variable graphed on the horizontal axis (x-axis) and the other variable graphed on the vertical axis (y-axis). Graphing data via a scatterplot allows us to see the overall pattern of the data, along with identifying any striking deviations from the pattern (outliers). The key features to look for in a scatterplot are Form, Direction, Strength, and Outliers. Form – Is the association between the variables linear, curved, or other? Direction – Is the association positive or negative? A positive association : As one variable increases, the other variable also increases in value A negative association : As one variable increases, the other variable decreases in value Strength – How much scatter is present? (a measure of how closely the points follow a clear form) Outliers – Points that lie outside the overall pattern of the data. (important to identify & research outliers) Clusters/SubGroups – When there are distinct groupings of some data points (separate the data into different groups and draw separate scatterplots for each cluster) When using scatterplots to show the relationship between two variables, we must distinguish between the explanatory (predictor) variable and the response variable. The explanatory variable explains (predicts) changes in the response variable. In other words, the response variable responds to changes in the explanatory variable. In algebra, we called the explanatory variable the independent variable, and the response variable is the dependent variable. (see pages 169-170) In a scatterplot, the explanatory variable is graphed on the horizontal axis (x-axis) and the response variable is graphed on the vertical axis (y-axis).
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2 Activity 1: The following table describes the ACT scores (from high school) and their undergraduate GPA (out of 4.00) for 15 randomly selected graduates receiving a bachelor’s degree from a major university last year. ACT 22 21 18 27 24 26 19 21 28 20 22 19 23 24 29 GPA 2.85 3.08 2.30 3.46 2.75 3.18 2.41 2.75 3.58 2.47 2.70 2.34 2.63 2.90 3.23 A. Which is the explanatory variable and which is the response variable? Explanatory Variable: Response Variable: B. Use your calculator to make a scatterplot of this sample data. Click on STAT/EDIT & enter the given data into two lists.
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Chapter7-9 - Chapter 7 (Scatterplots, Association,...

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