CRITICAI. VAIJFS OF ThF t DISTRIBITION 1. You are given the following data to estimate
the model Y=a+bX+ where a and b are the intercept and slope parameters and is the noise term
whose mean is zero and variance is 2. (a) (10 points) Given a random sample of size 4 above,
estimate a and b, that is, the intercept and the slope coefficient and denote them as a^ and b^. (b)
(10 points) Compute SSE, SSR, SST and R2. (c) (10 points) Calculate the estimated variance of
b^. (d) (10 points) Using the above data to estimate c and d in the following model, and denote
them as c^ and d^. What is the relationship between b^ and d^ ? How about a^ and c^ ? (e) (10
points) If the regression is changed to Y=e+fX+u where Y=lnY, what would be the interpretation
of the slope coefficient in equation (2)? Now if we also change X to X and the model becomes
Y=g+hX+ where X=lnX, what would be the interpretation of the slope coefficient in equation
(3)?.
CRITICAI. VAIJFS OF ThF t DISTRIBITION 1. You are given the followi.pdf
1. CRITICAI. VAIJFS OF ThF t DISTRIBITION 1. You are given the following data to estimate
the model Y=a+bX+ where a and b are the intercept and slope parameters and is the noise term
whose mean is zero and variance is 2. (a) (10 points) Given a random sample of size 4 above,
estimate a and b, that is, the intercept and the slope coefficient and denote them as a^ and b^. (b)
(10 points) Compute SSE, SSR, SST and R2. (c) (10 points) Calculate the estimated variance of
b^. (d) (10 points) Using the above data to estimate c and d in the following model, and denote
them as c^ and d^. What is the relationship between b^ and d^ ? How about a^ and c^ ? (e) (10
points) If the regression is changed to Y=e+fX+u where Y=lnY, what would be the interpretation
of the slope coefficient in equation (2)? Now if we also change X to X and the model becomes
Y=g+hX+ where X=lnX, what would be the interpretation of the slope coefficient in equation
(3)?
