Scatterplots Part 2

standardization

allows us to compare correlations between data sets where variables are measured in different units or when variables are different

categorical data

can be added to scatterplots to reveal trends and group the data into categories

categorical data

does not have an order on the x axis- we would end up with different forms

perfect linear relationship

extremes values where r= -1 and r= 1

outlier

falls outside the overall pattern or relationship

weak relationship

for any x, you might get a wide range of y values

r

has no units and does not change when we change the units of measurement of x, y, or both

strength of linear relationship

increases as r moves away from 0 and toward -1 or 1

r less than 0

indicates a negative association

r greater than 0

indicates a positive association

r

is always a number between -1 and 1

correlation r

is it calculated using the mean and the standard deviation of both x and y variables, not resistant to outliers

correlation

makes no distinction between explanatory and response variables, requires both variables to be quantitative

correlation r

measures the strength of the linear relationship between two quantitative variables

values of r

near 0 indicate a very weak linear relationship

strength

of the relationship between the two variables can be seen by how much variation, or scatter, there is around the main form

correlation r

r= 1/n-1

scatterplot

relationships require that both variables be quantitative (the order of data points is defined entirely by their value)

both variables

should be given a similar amount of space: plot roughly square, points should occupy all the plot space (no blank space)

strong relationship

you can get a pretty good estimate of y if you know x