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Chapter 2   Two Numerical Variables

2.1   Scatterplots and correlation

2.1.1   Scatterplots

In this exercise, you will complete a scatterplot by dragging the crosses for the last two observations.

2.1.2   Information from scatterplots

The exercises in this page expect you to interpret scatterplots in terms of the relationship between the variables, clusters and outliers. In the first exercise, the interpretation is in an application context, whereas in the second the interpretation is in generic terms.

2.1.3   Correlation coefficient, r

In this exercise, you will make a rough estimate of correlation coefficient by eye from a scatterplot.

2.1.4   Clusters, outliers and curvature

This exercise presents four scatterplots (one elliptical, one with an outlier, one with two clusters and one with curvature) and asks for these to be matched with the corresponding values of r.

2.2   Least squares

2.2.1   Explanatory variable and response

For several scenarios, you must identify the explanatory variable and response, then state whether the data are observational or experimental and whether the relationship is causal.

2.2.2   Drawing a straight line

This exercise shows the equation of a straight line and asks you to sketch it.

2.2.3   Slope and intercept

The exercises on this page do the inverse of the previous exercise -- you are shown a straight line and asked to find its equation.

2.2.4   Interpreting the slope and intercept

In this exercise, you are asked to select one of four statements that correctly describes the slope or intercept of a least squares line in the context of the data.

2.2.5   Residuals

This exercise requests the least squares residual for a cross on a scatterplot.

2.2.6   Residual plot

In this exercise, you must identify which of four scatterplots is the correct residual plot when a linear model is fitted to a data set.

2.2.7   Predictions

The exercise on this page gives a least squares line and asks for a prediction of the response, given the value of the explanatory variable.

2.3   Curvature, outliers and leverage

2.3.1   Regression problems

This exercise asks you to identify the difficulties with using the least squares line to predict Y at a given X from the data in a displayed scatterplot (an outlier, curvature, a high-leverage point or extrapolation).

2.3.2   Log transformations of X and Y

You are asked whether a logarithmic transformation of X or Y might linearise the data in a scatterplot (and also give constant variability).

2.3.3   Prediction from nonlinear model

In this exercise, a least squares line is fitted to a model that involves log(X) and/or log(Y). You are asked to use the equation of the line to predict Y from X.

2.3.4   Power transformations (advanced)

This exercise shows a scatterplot of Y vs X, followed by three scatterplots involving transformations of Y and X (log, square and square root transformations). You are asked to match the scatterplots to the transformations.