# notes 7 - omparing Two Quantitative Variables Submitted by...

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omparing Two Quantitative Variables Submitted by gfj100 on Fri, 10/30/2009 - 09:39 As we did when considering only one variable, we begin with a graphical display. A scatterplot is the most useful display technique for comparing two quantitative variables. We plot on the y-axis the variable we consider the response variable and on the x-axis we place the explanatory or predictor variable. How do we determine which variable is which? In general, the explanatory variable attempts to explain, or predict, the observed outcome. The response variable measures the outcome of a study. One may even consider exploring whether one variable causes the variation in another variable – for example, a popular research study is that taller people are more likely to receive higher salaries. In this case, Height would be the explanatory variable used to explain the variation in the response variable Salaries. In summarizing the relationship between two quantitative variables, we need to consider: 1. Association/Direction (i.e. positive or negative) 2. Form (i.e. linear or non-linear) 3. Strength (weak, moderate, strong) Example We will refer to the Exam Data set, ( Final.MTW or Final.XLS ), that consists of random sample of 50 students who took Stat200 last semester. The data consists of their semester average on mastery quizzes and their score on the final exam. We construct a scatterplot showing the relationship between Quiz Average (explanatory or predictor variable) and Final (response variable). Thus, we are studying whether student performance on the mastery quizzes explains the variation in their final exam score. That is, can mastery quiz performance be considered a predictor of final exam score? We create this graph using either Minitab or SPSS: Using Minitab Using SPSS 1. Opening the Exam Data set. 2. From the menu bar select Graph > Scatterplot > Simple 3. In the text box under Y Variables enter Final and under X Variables enter Quiz Average 4. Click OK

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Association/Direction and Form We can interpret from either graph that there is a positive association between Quiz Average and Final: low values of quiz average are accompanied by lower final scores and the same for higher quiz and final scores. If this relationship were reversed, high quizzes with low finals, then the graph would have displayed a negative association . That is, the points in the graph would have decreased going from right to left. The scatterplot can also be used to provide a description of the form . From this example we can see that the relationship is linear. That is, there does not appear to be a change in the direction in the relationship. Strength
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notes 7 - omparing Two Quantitative Variables Submitted by...

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