讲解Graphics留学生、R辅导、讲解R编程设计、辅导R scripts留学生
讲解Database|解析Java程序
1. Suppose X1, X2, . . . , X9 are iid N(μ, 4) variables. We wish to test H0 :
μ = 1 against H1 : μ = 3
(a) Calculate the size and power of the test with rejection region X >ˉ
2.
(b) Find k so that the test with rejection region X > k ˉ has size 0.05.
Calculate the power of this test.
2. The data set big.mac is part of a larger data set described in Cook and
Weisberg, “Applied Regression Including Computing and Graphics,”
Wiley, 1999.
Download the data file, the data is available on moodle. Read the data
into R.
The Big Mac hamburger is a simple commodity that is virtually identical
throughout the world. One might expect that the price of a Big
Mac should be the same everywhere, but of course it is not the same.
The Economist magazine has published a Big Mac parity index, which
compares the costs of a Big Mac in various places, as a measure of
inefficiency in currency exchange. We will use these data to study how
the cost of a Big Mac varies with economic indicators that describe
each city. The variables in the data are logBigMac (log of minutes of
labour required by an average worker to buy a Big Mac and french fries)
logBusFare (log of lowest cost of 10km public transit in US dollars)
logTeachSal (log of annual salary of a primary teacher in US dollars)
and logTeachTax (log of tax rate paid by a primary teacher).
For the following, please provide R scripts that you use and the corresponding
output, including any relevant graphs to support your answers.
(a) Fit a linear model with logBigMac as the response and the remaining
variables as predictors.
(b) Is there any evidence that any of the assumptions of the linear
regression model is not satisfied?
(c) Examine residuals and other diagnostics for the fitted model. Are
there any unusual or influential points?
2(d) Examine the summary output: based on the summary output, do
you think that any of the predictors could be deleted from the
model? Please state any relevant statistical tests you used to base
your conclusion on.
(e) Consider two alternative models: the model including all predictors,
and the model where the predictor logBusFare and logTeachTax
are deleted. Use the F statistic, stating clearly any hypothesis
being tested, and the conclusions reached regarding the two predictors.
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