Statistics - Unit 5

scatterplot

provides a way to study the relationship between two quantitative variables measured on the same subject or at the same time point

explanatory variable

plotted on the x-axis

response variable

plotted on the y-axis (may be impacted by explanatory variable)

form, association/direction, strength, and outliers

four key features of scatterplots

correlation (r)

for linear relationships between two numerical variables, strength can be formally measured using 

residuals

error between predicted values (ŷ) and the observed values (y)

e = y - ŷ

least squares regression (LSR) line

line of best fit that produces the “least squared” error as defined by the residuals

ŷ = a + bx

slope

b = r (sy/sx)

y-intercept

a = ŷ - bx

interpretation of the slope

as x increases by one unit, the predicted/average y increases/decreases by __ (slope) units

coefficient of determination

r²; the proportion of variation in y that is explained by the line with x

influential points

very large or very small x-value compared to the majority of the data

extrapolation

the practice of using the line of best fit to make predictions for values of x that were never modeled