Textbook Notes (363,264)
Economics (479)
ECO220Y1 (33)
Chapter 6

# ECO220Y1 Chapter 6 Notes Premium

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School
University of Toronto St. George
Department
Economics
Course
ECO220Y1
Professor
Jennifer Murdock
Semester
Fall

Description
ECO220Y1 Textbook Notes Chapter 6: Scatterplots, Association, and Correlation  Scatterplot: a graph that shows the relationship between two quantitative variables measured on the same cases. o It is easy to see patterns, trends, relationships, and even the occasional unusual values standing apart from the others by simply looking at one.  Association o Direction: a positive direction or association means that, in general, as one variable increases, so does the other.  When increases in one variable generally correspond to decreases in the other, the association is negative. o Form: the form we care about most is straight, but other patterns in the scatterplots should be described as well. o Strength: a scatterplot is said to show a strong association if there is little scatter around the underlying relationship. 6.1 Looking at Scatterplots  Outliers can lead us to probe further to understand our data more clearly.  There may be entire clusters or subgroups that stand away or show a trend in a different direction than the rest of the plot. o Try to understand why they are different and possibly split the data into subgroups to obtain a more relevant conclusion. 6.2 Assigning Roles to Variables in Scatterplots  Bivariate analysis: statistical analysis of two variables at the same time, as in our calculation of the correlation coefficient and plotting of scatter diagrams.  Explanatory (predictor/independent) variable: The variable that accounts for, explains, predicts, or is otherwise responsible for the y-variable. o It is the x-axis variable.  Response (dependent) variable: The variable that the scatterplot is meant to explain or predict. o It is the y-axis variable.  The roles that are chosen for each variable have more to do with how we think about them than with the variables themselves. o What are we trying to look for? 6.3 Understanding Correlation  Changing the units of either axis will not change the direction, form, and strength of the scatterplot.  The variables can be standardized for simplicity’s sake. ̅ ̅ ( )  By standardizing the values, the scales on both the x-axis and y-axis will be equal. o Equal scaling gives a neutral way of drawing the scatterplot and a fairer impression of the strength of the association.  By taking the products of each point of ( ) and summing them, we can get a measure of the strength of the association. o Points in the upper right and lower left sections of the plot will have the same signs and thus their products will be positive (positive correlation). o Points in the upper left and lower right sections of the plot will have the opposite signs and thus their products will be negative (negative correlation).  To adjust for the size of the sum since it gets bigger the more data that exists, divide the sum by . o This ratio is called the correlation coefficient, or just the correlation. o Correlation coefficient: a numerical measure of the direction and strength of a linear association. Other equivalent variations of the formula:
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