Multiple regression is always better than simple regression, providing a
sufficient number of data points available.
Increasing the sample size is the only way to increase the precision of the
interval while maintain the same confidence level.
A small investor is considering a $200 investment in growth stocks for two
years. Let X denote the gain in buying and holding for two year one $100
share of stock 1, and let Y be defined similarly for one $100 share of stock
2. Assume E(X) = 50 , E(Y ) = 50 , Var(X) = 64 , and Var(Y ) = 81 .
Consider the following options: (a) buy two shares of stock 1, (b) buy two
shares of stock 2, (c) buy one share each of stock 1 and 2. We can conclude
that all three options have the same expected gain.
Refer to Question 9, If Cov(X,Y ) = 60 , we can conclude that the option (a)
is less risky than options (c) and (b).
If the errors in the Classic Linear Regression (CLR) model are not
normally distributed, although the OLS estimator is no longer BLUE, it is
still unbiased.
A shoe salesperson has ten different boots to display in her showcase
window. She can display only four at one time. So there are 210 sets of four
boots can be selected.
Randomly choose 3 balls from a bag containing 5 red balls, 3 white balls
and 9 blue balls. The probability that at least one of the three is white is
0.464?
Suppose there are three events A, B, and C with probabilities: P(A) = 0.5,
P(B) = 0.4, P(C) = 0.3 , A and C are mutually exclusive; A and B are
independent; and P(B and C) = 0.05 . Let A′, B′ , and C′ be the
complement event of A, B, and C, respectively. We can calculate that
P(B′|A) is greater than 0.65.
The Chi-square test can be used to test whether sample data indicate that
a particular model for a population distribution does or does not fit the
data.
Suppose a researcher wants to conduct a study to estimate the population
mean. He plans to use a 95% level of confidence to estimate the mean, and
the population standard deviation is approximately 34. The researcher
wants the error to be no more than 4. The sample size should be at least
290.
If the ANOVA F test is significant in a single-factor completely randomized
design, multiple comparison test is appropriate for finding out which
treatment group means are significantly different from others.
A confidence interval for a normal population mean, 5 ± 0.6533 was
constructed with a sample of size 36 and a 0.95 confidence coefficient. If
the population variance was known, what is it?
4.2
4.1
4
2
2.1
Suppose P(A1 ) = 0.25 , P(A2 ) = 0.75 , P(B1|A1 ) = 0.10 and P(B1|A2 ) =
0.30, then P(A1|B1 ) = ?
0.100
0.250
0.173
0.211
0.025
The following data are obtained for estimation of the linear relationship.
Your estimate of β is?
2.1230
2.0898
1.965
2.0012
2.0792
The life of a light bulb in 1000hr. units gas a gamma distribution whose
mean is two and whose variance is four. The value of λ and α are?
1 & 1
1 & 0.5
2 & 1
0.5 & 2
0.5 & 1
The life of a light bulb in 1000hr. units gas a gamma distribution whose
mean is two and whose variance is four.
What is the probability that such a light bulb will have
a life time between 900 and 1100 hours?
e−0.45 − e−0.55
e0.45 − e0.55
e−0.55 − e−0.45
e−0.45 + e−0.55
e0.45 − e−0.55
(11.73, 37.87)
(12.73, 36.87)
(12.23, 37.87)
(11.73, 36.87)
(12.73, 35.87)
Given that X ~ N(10, 3) and Y ~ N(7, 4) , X and Y are independent.
What is the distribution of 3X −Y ?
N(22, 30)
N(23, 30)
N(23, 31)
N(22, 31)
N(23, 29)
Given that a joint p.d.f. f(x, y) = 2 , 0 ≤ x ≤ y ≤ 1 . What is the value of
E(X) and E(Y ) ?
1/4 & 2/3
1/2 & 1/3
1/3& 1/3
2/3 & 1/2
1/3 & 2/3
What is the value of Cov(X,Y ) and ρ xy ?
1/36 & 1/2
1/32 & 1/2
1/25 & 1/3
1/27 & 1/3
3/38 & 1/3
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