SOC101Y University of Toronto Robert Brym Online Mini-Lecture #6 Correlation Click icon to repeat audio Right cursor to advance ->

Scatterplot X Values Click icon to repeat audio Right cursor to advance -> Left cursor to go back <-

Scatterplot X Values Click icon to repeat audio Right cursor to advance -> Left cursor to go back <-

Scatterplot X Values Click icon to repeat audio Right cursor to advance -> Left cursor to go back <-

Scatterplot X Values The red “trend line” or “least-squares regression line” is drawn to minimize the sum of the squared distances between each point in the scatterplot and the line. Click icon to repeat audio Right cursor to advance -> Left cursor to go back <-

Correlation  r = correlation coefficient (a measure of the degree to which points are non-randomly scattered around the regression line) Click icon to repeat audio Right cursor to advance -> Left cursor to go back <-

Correlation  r can vary between -1 and 1  r = correlation coefficient (a measure of the degree to which points are non-randomly scattered around the regression line) Click icon to repeat audio Right cursor to advance -> Left cursor to go back <-

Correlation  r can vary between -1 and 1  The bigger the magnitude of r (the closer it is to -1 or 1), the less random the scatter and the stronger the association between two variables.  r = correlation coefficient (a measure of the degree to which points are non-randomly scattered around the regression line) Click icon to repeat audio Right cursor to advance -> Left cursor to go back <-

Correlation  r can vary between -1 and 1  The bigger the magnitude of r (the closer it is to -1 or 1), the less random the scatter and the stronger the association between two variables.  The smaller the magnitude of r (the closer it is to 0), the more random the scatter and the weaker the association between two variables.  r = correlation coefficient (a measure of the degree to which points are non-randomly scattered around the regression line) Click icon to repeat audio Right cursor to advance -> Left cursor to go back <-

Correlation  r can vary between -1 and 1  The bigger the magnitude of r (the closer it is to -1 or 1), the less random the scatter and the stronger the association between two variables.  The smaller the magnitude of r (the closer it is to 0), the more random the scatter and the weaker the association between two variables.  If r is positive, one variable is directly proportional to the other (as one increases in value, so does the other); thus the trend line slopes upward.  r = correlation coefficient (a measure of the degree to which points are non-randomly scattered around the regression line) Click icon to repeat audio Right cursor to advance -> Left cursor to go back <-

Correlation  r can vary between -1 and 1  The bigger the magnitude of r (the closer it is to -1 or 1), the less random the scatter and the stronger the association between two variables.  The smaller the magnitude of r (the closer it is to 0), the more random the scatter and the weaker the association between two variables.  If r is positive, one variable is directly proportional to the other (as one increases in value, so does the other); thus the trend line slopes upward.  If r is negative, one variable is inversely proportional to the other (as one increases in value, the other decreases); thus the trend line slopes downward.  r = correlation coefficient (a measure of the degree to which points are non-randomly scattered around the regression line) Click icon to repeat audio Right cursor to advance -> Left cursor to go back <-

Strong Positive Correlation r =.740 Failed test 1 and failed course Passed test 1 and failed course Failed test 1 and passed course Passed test 1 and passed course Final Grade Test 1 Grade Click icon to repeat audio Right cursor to advance -> Left cursor to go back <-

Moderately Strong Negative Correlation r = Happiness Household Income Inequality Click icon to repeat audio Right cursor to advance -> Left cursor to go back <-

Zero Correlation r = 0 Shoe Size IQ Click icon to repeat audio Right cursor to advance -> Left cursor to go back <-

Caution While a linear regression line may summarize the relationship between two variables, a curvilinear regression line may provide more information about the data in the scatterplot. Consequently, it is always necessary to inspect scatterplots visually and not just rely on statistical coefficients such as r to interpret the association. Click icon to repeat audio Right cursor to advance -> Left cursor to go back <-

SOC101Y University of Toronto Robert Brym Online Mini-Lecture #6 Correlation Left cursor to go back <- END