Correlation and functions

Pearson correlation coefficient (r)

conditions: random samples and independent observations
-normality of x and y
-linear trend
-no extreme outliers

properties of r

describes the strength of the linear relationships between 2 numbers
-unitless

range of r

between -1 and 1

interpretation of r

-1 or 1 means perfectly linear
-0 means no relationship
-absolute value indicates strength of linear relationship
-sign indicates direction

strong correlation

r value above .5
- ~.5-.6 is moderately strong

weak correlation

r value below .5

things that don't affect r value

-changing the order of variables
-adding or multiplying by a constant

things that do affect r's value

-influential outliers

correlation cautions

correlation does not equal causation
-x and y can switch and still get the same value
lurking variables

how to calculate r

(sum of zx*zy)/(n-1)
Remember to convert to z scores first!

interpretation

describe: strength, direction, define correlation as a measure of the linear relationship

functions

input only has one outputw

what type of data used to create a function?

two numerical variableswh

why are functions models useful?

1)gives us a characteristic rate of change
2) ability to predict future values

function notation

y=f(x)
dependent is a function of the indpendent

y

output/dependent

x

output/independent

linear relationship

y=b0+b1x

b1

slope: describes the constant rate of change in the dependent variable as the independent variable increases by one unit

b0

y-intercept: describes the value of the dependent variable when the independent variable equals zero