![]() ![]() ![]() 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. The correlation coefficient r measures the direction and strength of a linear relationship. 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. Graphically, correlation and regression analysis can be visualized using scatter plots. Other relationships may be nonlinear or non-monotonic. positive correlation: A positive correlation appears as a recognizable line with a positive slope. Both correlation and regression analysis are done to quantify the strength of the relationship between two variables by using numbers. Figure 8.65 A scatter plot is a visualization of the relationship between quantitative dataset. 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. In order for data to be shown on a scatter plot, it has to be measured in numerical values. If there is a relationship between the two variables, it will be shown on the scatter plot. If there is no pattern, the association is zero. Scatter plots are used to determine if there is a relationship between the two variables being studied. 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. A correlation coefficient is a bivariate statistic when it summarizes the relationship between two variables, and it’s a multivariate statistic when you have more than two variables. ![]()
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