Equations Flashcards
What is the equation for r?
r = ∑(Xi - X̄) (Yi - ȳ) / (n-1) SxSy
What is the linear regression model equation?
(What does Yi = ?)
Yi = b0 + b1Xi + ei
where:
Yi = dependent variable
b0 = population y intercept
b1 = population slope coefficient
Xi = independent variable
ei = random error term
In the equation:
Yi = b0 + b1Xi + ei
WHAT DOES Yi = ?
Yi = dependent variable
In the equation:
Yi = b0 + b1Xi + ei
WHAT DOES b0= ?
b0 = population y intercept
(the intercept)
In the equation:
Yi = b0 + b1Xi + ei
WHAT DOES B1 = ?
b1 = population slope coefficient
(the slope)
In the equation:
Yi = b0 + b1Xi + ei
WHAT DOES Xi = ?
Xi = independent variable
In the equation:
Yi = b0 + b1Xi + ei
WHAT DOES ei = ?
ei = random error term
What is the simple linear regression equation / prediction line?
(What does Ŷi = ?)
Ŷi = b0 + b1Xi
where:
Ŷi = estimated/predicted Y value for observation i
b0 = estimate of the regression intercept
b1 = estimate of the regression slope
Xi = value of X for observation i
What does Ŷi = ? in
Ŷi = b0 + b1Xi
Ŷi = estimated/predicted Y value for observation i
What does b0 = ? in
Ŷi = b0 + b1Xi
b0 = estimate of the regression intercept
What does b1 = ? in
Ŷi = b0 + b1Xi
b1 = estimate of the regression slope
What does Xi = ? in
Ŷi = b0 + b1Xi
Xi = value of X for observation i
What is b1 and how do you work it out?
b1 = r (Sy / Sx)
(the slope)
where:
r = the correlation coefficient between Y and X
Sy = the standard deviation of Y
Sx= the standard deviation of X
ȳ = the average of y
x̄ = the average of x
What is b0 and how do you work it out?
b0 = ȳ - b1x̄
(the intercept)
where:
r = the correlation coefficient between Y and X
Sy = the standard deviation of Y
Sx= the standard deviation of X
ȳ = the average of y
x̄ = the average of x
