96年國立成功大學國際企業研究所統計學線上測驗

2.: We always assume the multiple regression equation we are estimating
includes all the relevant explanatory variables. In practice, this is rarely
the case. Sometimes some relevant variables are not included due to lack of
measurement. At other times some irrelevant variables are included. (20%)
(1) What are the consequences? (Hint: are the estimates still unbiased and
efficient when we omit some relevant variables or include some
irrelevant variables? Why?). (10%)
(2) One student says: “it is better to include variables (when in doubt)
rather than exclude them”. Do you agree him? Why? (10%)

3.: When we run the regression equation, we always assume the errors are
independent. (40%)
(1) In practice, is the assumption reasonable? Please provide an example.
(2) The Durbin-Watson (DW) test is the simplest and most commonly test
for the errors. Please provide a detail description to it. (5%)
(3) If the DW test statistics is significant, could we conclude the errors are
not independent? Why? (10%)
(4) If the errors are not independent, what are the consequences? (10%)
(5) Following with (4), what are the solutions? (10%)

4.: There are some probability distributions for which the probabilities have
been tabulated and which are considered suitable descriptions for a wide
variety of phenomena. These are the normal distribution, and the X² , t,
and F distributions. (15%)
(1) Please describe the normal distribution in detail. (5%)
(2) As is well known, the X² , t, and F distributions could be derived from
the normal distribution. Please describe the procedures in detail. (10%)

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