Textbook Notes (363,264)
Canada (158,281)
Economics (479)
ECO220Y1 (33)
Chapter 6

ECO220Y1 Chapter 6 Notes

4 Pages
Unlock Document

University of Toronto St. George
Jennifer Murdock

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:
More Less

Related notes for ECO220Y1

Log In


Don't have an account?

Join OneClass

Access over 10 million pages of study
documents for 1.3 million courses.

Sign up

Join to view


By registering, I agree to the Terms and Privacy Policies
Already have an account?
Just a few more details

So we can recommend you notes for your school.

Reset Password

Please enter below the email address you registered with and we will send you a link to reset your password.

Add your courses

Get notes from the top students in your class.