Please helps, please write out any formulas if needed for explanations How do yo
ID: 2506181 • Letter: P
Question
Please helps, please write out any formulas if needed for explanations
How do you interpret the large increase in R2 from Model (1) to Model (2)? f) (5) Notice the continual decline of the coefficient estimate for studpc as I progress from Model (1) to Model (3). Can I say that my estimate for studpc is closer to the truth in Model (3) than in Model (1)? Why or why not? Suppose I reestimate Model (1) except that I replace totday with the logarithm of totday. Doing this provides a coefficient estimate of 9.698. Please interpret this coefficient estimate appropriately and compare it to your original interpretation. Is the fact that the standard deviation for the coefficient estimate for totday between Model (1) and Model (3) decreased an indication that studpc is collinear with the other variables in the model? Comment on the likely presence of collinearity between lnchpct and sttchratio. Use the standard errors from Models (2) and (3) to aid your discussion. Consider the following model: y= beta 0 = beta 1 x1 +beta 2x2 + eplision; var(eplision|x1,x2) = sigma2. The conditional variance of the OLS estimator of beta i is Explain what each of these three components in the conditional variance are and how each influences the conditional variance of the estimator.Explanation / Answer
e)A large increase in R^2 from model 1 to model 2 can be interpreted as due to introduce of lunchpct variable in model 2, goodness of fit of data has increased.i.e model2 became more efficient in fitting the data.
f)Yes there is continual decline of coefficient estimate of studpc from model 1 to model3.In model 3 it is closer to truth as R^2 of model 3 is high and also statistical significance of coefficients increased.So coefficient of studpc in model 3 is closer to truth.
g)In model 1 it says that if totday increases by 1 unit ,dependent variable totsc4 decreases by 0.002 times as its coefficient is -0.002.But due to introduction of log it is interpreted as percentage change.So coefficient of 9.698 indicates,if totday changes by 1% tentosc4 changes by 9.968 times .
as coefficient in log model = dy / (dx/x)
h) Yes its true, decrease of standard deviation from model 1 to model 3 indicates is an indication that it is collibnear with other variables as
standard deviation is proportional to 1/sqrt(1-r^2) where r represent strength of linear relationship
6) conditional variance depends on 3 terms, one is R^2 which represents correlation between independent variables 1 and 2. So when R^2 increases conditional variance decreases as R^2 is in denominator and other term is variance of x which is sum of (xi-xbar)^2 , where xbar- mean of x.
As variance of x is in denominator ,if it increases then conditional variance decreases. and other term it depends is variance of dependent variable which if it increases, conditional variance increases