ENVS 203 Week 3

scatterplot (numeric, 2 variables)

primary tool for examining 2 variable relationships when both variables are numerical

how to describe scatterplots

trend, strength, shape

scatterplot trend

positive or negative associations

positive associations

increasing trends

negative associations

decreasing trends

scatterplot strength

weak association (more spread) or strong association (less spread or little vertical variation)

scatterplot shape

linear or nonlinear

correlation coefficient (r)

a number that measures the strength of the linear association between 2 numerical variables

always between [-1, 1]

correlation does NOT mean causation

only for LINEAR associations

ALWAYS make a graph of the data to see if it's linear

positive r

indicates a scatterplot with a positive trend

negative r

indicates a scatterplot with a negative trend

if r is close to -1 or 1

strong association

if r is close to 0

weak association

regression analysis

estimating the relationship between a dependent variable and one or more independent variables

we will use a model of the data and interpret that

be aware of OUTLIERS

model

a representation of observed data

will consist of an equation and a set of conditions

regression line

a tool for making predictions about future observed values

the line that comes closest to most of the points

y \= a + bx

a \= intercept
b \= slope/coefficient

least squares principle

how we find the line that is closest to most of the points

the difference between your observation and calculation based on the line function will be the smallest

coefficient of determination

the correlation coefficient squared

in the range of [0,1]

measures how much of the variation in the response variable is explained by the explanatory variable