Week 7 Flashcards
What did francis galton do in 1886
Created a graph representing peoples height and their parents height
How to calculate correlation
r = Sxy/Sx.Sy
Sxy = how much x and y change together
Sx.Sy = how much x and y change separately
What is the r squared value and how is it calculated
The r-squared value tells you (just the r value squared):
How much of the variance is explained by your correlation
If your r-squared valye is close to 1…
your correlation explains a lot of variance
What is the r-squared value sometimes called
Coefficient of determination
What does the r value go from?
-1 to 1
What does the r squared value go from
0 to 1
1-r sqaured is
The amount of variance not explained.
e.g.if height explains half the data, then what explains the other half
Regression facts
When x=0, y=intercept
When x increases by 1, y increases by the slope
y = mx+c
y = what the y axis is
m = slope
x + what the x axis is
c = y intercept
Are X and Y interchangeable in regression
No, only in correlation
What is the formula for reporting correlations
r (df) = (pearsons r), p (p value)
Degree of freedom for correlations
Total number minus 2
Reporting regressions
Overall results = r squared value
Model fit results = F (df1), (df2) = F value, p value
How to calculate the t value
t = estimate / SE
Difference between correlation and regression
Correlation describes a single relationship
Describes the direction and strength of a relationship
X and Y are inter-changeable and does not allow predicition
regression can describe multiple relationships
It describes the directionS and strengthS of relationships, X and Y are not interchangeable and it allows prediciton
Regression and correlation both
Involve linear relationships between one or more input
(predictor) variables and a single output (outcome) variable
Multiple regression
A single outcome variable (y)
Multiple predictor variables (x1, x2)
Residuals are distances from the surface
