The maximum likelihood estimators of β1 and β0 are unbiased and have
minimum variance among all unbiased linear estimators.
β1 indicates the change in the mean of the probability distribution of response
variable per unit increase in predictor variable.
The 95 percent prediction interval for the mean of 3 new observations for given
Xh is wider than that obtained for a new observation Yh(new) .
Let X be a random variable with mean μ , and the variance of X , denoted by
Var(X ) . Please define a reasonable way of measuring the possible variation of X .
Explain your answer (in Chinese or English and/or figure)! (25%)
Suppose that the number of kilometers that a car can run before its battery wears out is
exponentially distributed with an average value of 10,000 kilometers. If a person desires
to take a 5000-kilometer trip, what is the probability that he or she will be able to
complete the trip without having to replace the car battery? (25%)
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