Note the range of each variable, and add tick marks and scales to each axis. Drawing scatterplots.ĭecide which variable should go on each axis, and draw and label the two axes. In this example, the variables could be switched since either variable could reasonably serve as the explanatory variable or the response variable. The variable that is suspected to be the response variable is plotted on the vertical (y) axis and the variable that is suspected to be the explanatory variable is plotted on the horizontal (x) axis. In our example the two observations correspond to a particular email. In unpaired data, there is no such correspondence. We say observations are paired when the two observations correspond to the same case or individual. Since there are 50 cases in email50, there are 50 points in Figure 2.1.1. In any scatterplot, each point represents a single case. A scatterplot is shown in Figure 2.1.1, illustrating the relationship between the number of line breaks ( line_breaks) and number of characters ( num_char) in emails for the email50 data set. When we talk of a relationship or an association between variables, we are interested in how one variable behaves as the other variable increases or decreases.Ī scatterplot provides a case-by-case view of data that illustrates the relationship between two numerical variables. Sometimes researchers wish to see the relationship between two variables. Subsection 2.1.2 Scatterplots for paired data ¶ Read and interpret a cumulative frequency or cumulative relative frequency histogram. Also, identify whether a distribution is unimodal, bimodal, multimodal, or uniform. Identify the shape of a distribution as approximately symmetric, right skewed, or left skewed. Be able to read off specific information and summary information from these graphs. Understand what the term distribution means and how to summarize it in a table or a graph.Ĭreate univariate displays, including stem-and-leaf plots, dot plots, and histograms, to visualize the distribution of a numerical variable. Describe the direction, form, and strength of the relationship, as well as any unusual observations. Use scatterplots to represent bivariate data and to see the relationship between two numerical variables. We will apply these techniques using county-level data from the US Census Bureau, which was introduced in Section 1.2, and a new data set email50, that comprises information on a random sample of 50 emails. How do we visualize and describe the distribution of household income for counties within the United States? What shape would the distribution have? What other features might be important to notice? In this section, we will explore techniques for summarizing numerical variables. D Calculator reference, Formulas, and Inference guide.C Calculator reference, Formulas, and Inference guide.Inference for the slope of a regression line.Fitting a line by least squares regression.Line fitting, residuals, and correlation.Inference for the difference of two means.Inference for a mean with the \(t\)-distribution.Testing for goodness of fit using chi-square.Sampling distribution of a sample proportion.Case study: malaria vaccine (special topic).Observational studies and sampling strategies.Case study: using stents to prevent strokes.
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