Scatterplot ch 6 stats

Relationships

Most statistical relationships involve more than 1 variable so it is common to use bivariate data(2 variables)

Explanatory variable

Observed outcome w/ x variable

Response variable

Measures outcome of study w/ y variable

Scatter plot

graph displays direction, form, strength of a relationship btw 2 quantitative variables

Purpose of scatter plot

Display wat happens wen explanatory variable changes

Best fit line

line drawn btw points that form the scatter plot, to show direction of the relationship btw points

No association

Wen x value up, y value random up&down

Non linear association

wen 2 variables form clear pattern but not a straight line

Perfect association

wen points exactly on best fit line and resemble y=mx+b

Purpose of scatter plot and its best fit line

help validate hunches, display direction & strength of associations

Correlation aka

Pearson correlation

Correlation made by

Karl Pearson

Correlation

Determine numeric association which is strength & direction of set data

Correlation equation

r = (sum of sx*sy)/n-1

spread of r

always btw -1 and 1

0 - .20

no/random association

.20-.40

very weak association

.40-.60

weak association

.60-.80

moderate association

.80-.95

strong correlation

.95-1

very strong correlation

R rules

1. No unit & doesn’t change wen we change units

2. Not for non linear functions

3. Strongly influence by outliers like standard deviation and mean

4. Doesn’t prove causation

5. Multiply in equation order doesn’t matter

Least squares regression line

LSRL and technical term of best fit line and predicts how response variable changes explanatory variable

LSRL equation

ŷ = a + bx 

LSRL y- intercept and slope

Interpreting slope

Interpreting slope in written

for every one extra change in x, the number of y changes

Interpolation

Predicting y value with data in spread

Extrapolation

Don’t calculate and predicts it for data not in spread