If you got random draws from a Bivariate Normal (for example plotting the combination of weight...
If you got random draws from a Bivariate Normal (for example plotting the combination of weight and height of random people) and plotted them in an x1 vs. x2 scatterplot. Plot how they look like if the correlation coefficient for x1 and x2 was equal to 0, 0.5 and 1?
Homework Answers
The correlation coefficient is the parameter for the linear relationship between the two variables which ranges from -1 to +1.
- For a value of 0, it means that there is no linear correlation
between the two variables and therefore the scatter plot will show
no correlation as:
- For a correlation coefficient of 0.5, this means it lies in the
middle of 0 and 1 which suggest a moderate positive correlation
between the two variables. This is shown in the scatter plot here
as:
- For a correlation coefficient of 1, there is a perfect positive
correlation between the two variables, that is they all lie on the
straight line. As one variable x1 increases, the other also
increases while as one decreases, the other also decreases
perfectly. This is shown on a scatterplot as:
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