answer True or False and explain the answer

Assignment
Topic: True or False based On Linear Regression
Submitted To:
Submitted By:
Date: 06/03/2021
a)
Suppose we have a new value of x, call is Xnew and we want to predict the corresponding Ynew using a regression model. Prediction uncertainty for Ynew does not depend on the value of Xnew.
Ans: False
Explanation: As the prediction uncertainty of the dependent variable depends on the error term as well as the value of X. Thus, any uncertainty in the prediction depend on the value of Xnew.
b)
If the assumptions are met, then the least squares residuals are correlated with the fitted values.
Ans: False
Explanation: let e be the residual and is the fitted value. By the definition of covariance
Hence, if the covariance between these two are 0. Then we can say that the correlation will be 0. Thus, the above statement is false.
c)
A confidence interval for is centered at .
Ans: False
Explanation: The value of the confidence interval for is always centered around the value of the not at . Because the formula for confidence interval for is . Thus, the standard error SE(beta-1) and are small values. Thus, the value always centered around the original value of .
d)
It is possible to reject the null hypothesis when the null hypothesis is true.
Ans: True
Explanation: It is possible to reject the null hypothesis if it true. Which is a case of type 1 error. In statistics type 1 error is possible. When we reject the null hypothesis under a certain level of significance.
e)
least square...