Use this scatterplot to answer the following questions. She plotted the data in the scatterplot below. In order to better predict her costs, she has been collecting data on the number of books in each shipment she has sent and the weight of the shipment. ExampleĬaitlyn has started a business selling textbooks and novels online. For scatterplots with linear patterns, the correlation coefficient can be used to better understand this strength. It can be somewhat subjective to compare the strength of one association to another. This is true whether the pattern is linear, nonlinear, positive, or negative. The strength of the relationship or association between two variables is shown by how close the points are to each other. This is seen as a linear pattern that falls from left to right. In a negative pattern, as the predictor increases, the value of the response decreases. This shows up in the scatterplot as a linear pattern that rises from left to right. In a positive pattern, as the value of the predictor increases, so does the value of the response. If there is no clear pattern, then it means there is no clear association or relationship between the variables that we are studying.Īs you can see above, linear patterns can be thought of as either positive or negative. Whatever the pattern is, we use this to describe the association between the variables. Scatterplots with a linear pattern have points that seem to generally fall along a line while nonlinear patterns seem to follow along some curve. In general, you can categorize the pattern in a scatterplot as either linear or nonlinear. Each point represents the value of the response for a given value of the predictor. Using this terminology, a scatterplot is used to understand how the response responds to changes in the predictor. 2022.Īll rights reserved.Given a scatterplot, the variable on the horizontal axis is the predictor (or independent variable) and the variable on the vertical axis is the response (or dependent variable). Outliers can badly affect the product-moment correlation coefficient, whereas other correlation coefficients are more robust to them. An individual observation on each of the variables may be perfectly reasonable on its own but appear as an outlier when plotted on a scatter plot. If the association is nonlinear, it is often worth trying to transform the data to make the relationship linear as there are more statistics for analyzing linear relationships and their interpretation is easier thanĪn observation that appears detached from the bulk of observations may be an outlier requiring further investigation. The wider and more round it is, the more the variables are uncorrelated. The narrower the ellipse, the greater the correlation between the variables. If the association is a linear relationship, a bivariate normal density ellipse summarizes the correlation between variables. The type of relationship determines the statistical measures and tests of association that are appropriate. Other relationships may be nonlinear or non-monotonic. When a constantly increasing or decreasing nonlinear function describes the relationship, the association is monotonic. When a straight line describes the relationship between the variables, the association is linear. If there is no pattern, the association is zero. If one variable tends to increase as the other decreases, the association is negative. If the variables tend to increase and decrease together, the association is positive.
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