Fichas
Regression - Chapter Two
Fichas del conjunto (11)
- 1CORRELATION The total variation in y is measured by what?Syy = SIGMA(i=1,n)[(yi-ybar)^2
- 2We know that RSS = ? Where RSS is ... What can Syy be rewritten as ? Where Syy is ... Sxy^2/Sxx is ... and RSS is ...RSS = Syy - Sxy^2/Sxx
... SIGMA(i=1,n)[yi-B0hat-B1hat*xi]^2
Syy = RSS + Sxy^2/Sxx
... the variation in y ... the variation in y due to x ... unexplained variation - 3The proportion of variation in y which is explained by x can be written as what? What is this proportion often referred to as?Variation in y due to x/Total variation in y = (Sxy^2/Sxx)/Syy = Sxy^2/(Sxx*Syy)
R squared - 4The sample correlation coefficient, r, is defined as what? What can this also be rewritten as?r = sqrt(Sxy^2/(Sxx*Syy) = Sxy/sqrt(Sxx*Syy)
Sxy/sqrt(Sxx*Syy) = (Sxy/Sxx)*sqrt(Sxx/Syy) = B1hat*sqrt(Sxx/Syy) - 5The sign of r is the same as the sign of what 2 things? Since r^2 is a proportion what are the limits for r^2 and r? In what case does r=1 or r=-1? What name is r often referred to as?Sxy and B1hat
0 - 6On a scatter plot what happens with y and x: a) When r is positive b) When r is negative c) When r=0a) y increases with increasing x
b) y decreases with increasing x
c) There is no relationship between x and y - 7What happens to the correlation when a scatter plot has a horizontal line?The correlation is undefined as there is no variation in y
- 8CORRELATION, COVARIANCE AND INDEPENDENCE The sample correlation coefficient is? The population covariance of a) sigma(x^2) = ? b) sigma(y^2) = ? c) sigma(xy) = ? The population variance (p) = ?r= Sxy/sqrt(Sxx*Sxy)
a) sigma(x^2) = E[X-E(X)]^2
b) sigma(y^2) = E[Y-E(Y)]^2
c) sigma(xy) = E[(X-E(X))(Y-E(Y))]
p = sigma(xy)/sqrt[sigma(x^2)*sigma(y^2)]
THE POPULATION VARIANCE IS WHAT r IS MEASURING - 9If X and Y are independent random variables then Pr(X=x,Y=y) = ? For independent X and Y sigma(xy) = ? If two random variables are independent then their covariance and hence correlation is ... since ...Pr(X=x,Y=y) = Pr(X=x)Pr(Y=y) so
E(XY) = E(X)E(Y)
sigma(xy) = E[(X-E(X))(Y-E(Y))] = E[X-E(X)]*E[Y-E(Y)] = [E(X)-E(X)]*[E(Y)-E(Y)] = 0
... 0 ... p = sigma(xy)/sqrt[sigma(x^2)*sigma(y^2)] = 0/sqrt[sigma(x^2)*sigma(y^2)] - 10The converse - if two random variables have a correlation zero means ... There is a partial converse, what is it?... they aren't necessarily independent
If the random variables are normally distributed and have zero correlation then they are independent - 11Although a value of r close to 1 does indicate a strong positive linear association, a linear relationship is not always the most appropriate therefore what should you always do to check?Produce a plot of y against x (and plot a fitted straight line and see what the true model is)
Información
- Descripción
- Fichas sobre Regression - Chapter Two, creado por Cara Wales el 16/05/2016.
- Creado por
- Cara Wales
- Visitas
- 1
- Valoración