Correlation and regression Flashcards
What did Galton do in 1886?
Plotted to create idea of correlation
what were the first statistics invented analysing
co-relationships
What are key signs theres a mistake in data?
Perfect straight line
One or more datapoints far from others
No relationship at all
How does correlation find a best fit line?
By minimising differences between data and line
what is the equation for best fit line
r
r = Sxy ( how much x and y change together) / Sx.Sy (how much x and y change separately)
what does an r-value indicate
the direction of the qualification
R>0 = positive
R<0 = negative
Strength of correlation
closer to 1 is strong
closer to 0 is weak
What is used to show correlation explanatory power
r2
what is r squared also referred to as
coefficiant of determination
what does r squared indicate
how much variance is explained by the correlation
r squared close to one means lots of variance explained by correlation
r squared close to zero means little variance explanation
What is the regression equation
response variable / dependent variable = population Y intercept + population slope coefficient (independent variable) + error in equation residual
What are the key differences between correlation and regression
Describes single relationship
Direction of relationship
Strength of relationship
X & Y inter-changeable
r, r2
Does NOT allow prediction
Can describe multiple relationships
Directions of relationships
Strengths of relationships
X & Y NOT inter-changeable
R, R2, F, t, SE, ß1-n
Allows prediction
what is r represented as in jamovi
pearson’s r
In a correlation matrix what indicates df
It is calculated by N-2
How are correlations reported?
r (df) = pearson’s r, p = (p-value)
e.g.
r (64) = .881, p <.001
How is regression shown in jamovi for overall
R2 ,
model fit results
R2 = (r” value)
F (df1), (df2), = (F-value), p= (p-value)
e.g. F(1,64) = 233, p<.001
