Correlation coefficient- measures the strength of the linear association between variablesNonlinear relationships- the correlation coefficient doesn't helpTo find correlation coefficient- for each individual in the data set, you subtract the mean of the x variable from that individual’s value on x and divide by the standard deviation of x (and do the same thing for y for that individual). Then you multiply the x and y togetherMeasure of how far the individual’s value is from the mean above the mean would be positive, below the mean would be negativeOnce you get the product for z-score x and z-score y for each individual n the data set, you then add all of these up and divide by the number of individuals minus 1Important points about the correlation coefficient:Value ranges between -1 and 1 ONLYNegative values go with negative associationsPositive values go with positive associationsValues closer to 1 or -1 mean there’s a stronger associationValues near 0 mean there’s a weak associationStrong association- all the points fall close to a line that you could draw through the dataIf the points are evenly scattered, the correlation would be zero, and there would be no positive or negative associationThe correlation coefficient can be very strongly influenced by just a few outliers in the relationship between two variablesCan be strongly influenced by points that are outliers along one of the variables even if their not outliers of the relationship (an extreme value on x or extreme value on y can have a strong impact on the correlation coefficient)Answer to slide 41: AB is curvilinear, C shows a graph with a correlation of basically 1 and an outlier that is reducing the correlation, D has a correlation of zero if you take out the outlier, the outlier increases the correlation. If the points line up in a vertical line, the correlation is zeroCorrelation does not imply causation! By using scatterplots to show the relationship between two variables, we aren’t implying that there is a direct causal relationship between the variablesVariables can be associated in many ways:There is a direct causal relationshipThere is an indirect causal relationship (not direct causation of one to another)There is some third variable that influences bothRelationships Between Quantitative Variables 02/12/2014-Correlation coefficient- measures the strength of the linear association between variables -Nonlinear relationships- the correlation coefficient doesn't help-To find correlation coefficient- for each individual in the data set, you subtract the mean of the x variable from that individual’s value on x and divide by the standard deviation of x (and do the same thing for y for that individual). Then you multiply the x and y together-Measure of how far the individual’s value is from the mean above the mean would be positive, below the mean would be negative -Once you get the product for z-score x and z-score y for each individual n the data set, you then add all of these up and divide by the number of individuals minus 1-Important points about the correlation coefficient:-Value ranges between -1 and 1 ONLY-Negative values go with negative associations-Positive values go with positive associations-Values closer to 1 or -1 mean there’s a stronger association-Values near 0 mean there’s a weak association -Strong association- all the points fall close to a line that you could draw through the data-If the points are evenly scattered, the correlation would be zero, and therewould be no positive or negative association-The correlation coefficient can be very strongly influenced by just a few outliers in the relationship between two variables -Can be strongly influenced by points that are outliers along one of the variables even if their not outliers of the relationship (an extreme value onx or extreme value on y can have a strong impact on the correlation coefficient)-Answer to slide 41: A -B is curvilinear, C shows a graph with a correlation of basically 1 and an outlier that is reducing the correlation, D has a correlation of zero if you take out the outlier, the outlier increases the correlation. If the points line up in a vertical line, the correlation is zero-Correlation does not imply causation! By using scatterplots to show the relationship between two variables, we aren’t implying that there is a direct causal relationship between the variables -Variables can be associated in many ways:-There is a direct causal relationship -There is an indirect causal relationship (not direct causation of one to another)-There is some third variable that influences