KIN 4310 Lecture 7 Outline of Last Lecture I Frequency Distribution II Making Frequency Tables III Reading Histograms IV Different types of plots frequency polygon dot plot stem and leaf plot pareto chart pie chart scatter plot box plot time series graph other V Misuses of Statistics and Misleading Graphs VI Experimental Research variables and correlation Outline of Current Lecture VII Correlation Current Lecture o Correlation A correlation is a relationship between two variables can be generated for predicting the value of one variable given the value of the other variable This is appropriate for sample data that come in pairs Correlation Research o investigates a linear relationship between two variables o Variables must be continuous o Data can be presented graphically scatter plot o Neither variable is truly the independent or dependent variable o Called a bivariate relationship o There is no causation o Positive correlation indicates that when X increases so does Y o Negative correlation indicates that when X increases Y decreases and vice versa Linear correlation coefficient r a numerical measure of the strength of the relationship between two variables representing quantitative data Requirements The sample of paired x y data is a random sample of independent quantitative data Visual examination of the scatterplot must confirm that the points approximate a straight line pattern The outliers must be removed if they are known to be errors The effects of any other outliers should be considered by calculating r with and without the outliers included The coefficient of determination r2 the proportion of the variation in y that is explained by the linear relationship between x and y o Common errors involving correlation Causation It is wrong to conclude that correlation implies causality o Averages Averages suppress individual variation and may inflate the correlation coefficient o Linearity There may be some relationship between x and y even when there is no linear correlation Excel Function o CORREL array1 array2 These notes represent a detailed interpretation of the professor s lecture GradeBuddy is best used as a supplement to your own notes not as a substitute