# Conditional expected value from a regression model using ordinary least squares

I have a query regarding part (a) of the following question. I cannot figure out how to calculate the conditional expected value of collections for the month of Easter. Is it not possible to calculate the expected value for (a) with the given information, as no dataset is given with the question, is it possible to calculate the expected value for (a) without any data / only using the info provided below? If so could somebody point me in the right direction of how this would be done?

Any assistance or direction would be much appreciated.

4. Suppose you were recently hired to be the controller for a religious order. Since your duties include managing short-term cash flows, you need a forecast of the timing and magnitude of offerings. You expect Easter Sunday will be an event in which attendance and general offerings are expected to be above normal.

To estimate the Easter Sunday effect on order cash flows, you estimate the following regression model using ordinary least squares:

   COLLt  = b0 + b1 TIME + b2 DEaster + et

Where:
COLLt  = Monthly collections donated for general budget;
Time = Time index;
DEaster = Dummy variable equal to 1 for the month in which Easter occurs
and zero otherwise.


(a) What is the conditional expected value of collections for the month in which Easter occurs?
(b) Your expectations are that collections will be above normal for the month in which Easter occurs. Describe how you would test for this effect. Be specific in your description of testing procedures.

Therefore would (a) be something like: $E(X|Y=y) Coll_{t} = B_{0} + B_{2}(1) + E_{t} X = B_{0} + B_{2}(1) + E_{t}$

or would you keep the B1 slope & time index also so answer is: $X = B_{0} + B_{1} Time + B_{2}(1) + E_{t}$

Also in regards to part (b) the only way i can think of testing this is by comparing each month against easter to determine if the collections were above normal or comparing average collections from every month but easter against the easter collections. Any assistance with this would be great, stats is so difficult.