Eco 320 Spring 2003
Suggested questions for test
# 2 to be held on 04/09/2003
1.
A
psychologist employed by the director of human resources at the Hogan
Corporation obtained the IQ (X variable) and test scores (Y variable) of 14
industrial sales representatives. Based on these data, the following results
were obtained:
Mean of X = 111.428, Mean of Y = 70.643;
S XiYi = 113,355; S Xi2 = 176,928; S
Yi2 = 73293
Calculate the sample regression of Y on X:
Calculate the sample regression of X on Y.
2.
The
following data are obtained concerning the R&D expenditures and sales of
six telecommunication firms:
------------------------------------------------------
Firm ………….Sales ……R&D Expenditure
(in millions of dollars)
------------------------------------------------------
AT&T
50,790
419
Comsat
300
12
GTE
9,980
162
Rolm
201
13
United
1,904
3
Western Union
794
5
(a) Construct a scatter diagram of these data.
(b) Which variable (Sales or R&D) do you regard as the dependent variable?
(c) Compute the sample regression line: Yhat = a + b X
(d) Predict the average R&D expenditure if sales equal $15 million.
3.
Which
of the following is not an assumption on which regression analysis is based?
(a) The mean value of the dependent variable is a
linear function of the independent variable.
(b) The standard deviation of the conditional
probability distribution is the same regardless of the specified value of the
independent variable.
(c) The values of the dependent variable are
independent of one another.
(d) The independent variable is a random variable.
(e) None of the above.
4.
In
the general expression for the sample regression line Y = a + bX how do you
measure the change in the predicted value of Y associated with a one-unit increase in X?
(a)
By
the intercept term a.
(b)
By
the slope coefficient b.
(c)
By
the value of the dependent variable predicted by the regression line Y_hat.
(d)
By
the error term e.
(e)
None
of the above.
5.
In
regression analysis, what is the difference between Y and Yhat?
(a) Y denotes the intercept of the regression line
and Yhat denotes the slope of the line.
(b) Y denotes the slope of the regression line and
Yhat denotes the intercept.
(c) Y denotes an observed value of the dependent
variable and Yhat denotes its computed or estimated value.
(d) Y denotes the computed or estimated value of the
dependent variable and Yhat denotes its observed value.
(e) None of the above.
6.
In
the expression for the sample regression line Yhat = a + bX, the estimation of
a regression line amounts to the choice of numerical values of
(a) a and b.
(b) Yhat and X.
(c) b and X.
(d) X only.
(e) none of the above.
7.
"The
method of least squares dictates that we choose the line “where ______________
is a minimum."
(a) the sum of the squared deviations of the points
from the line
(b) the sum of errors
(c) the sum of the squared differences between the dependent
and independent variables
(d) the sum of the products of the dependent and independent
variables
(e) none of the above
8.
In
a least-squares regression of Y on X, the calculated value of b was 1.60 and
the calculated value of a was 4.83. What is the predicted value of Y if X
equals 22.70?
(a) 6.43.
(b) 16.27.
(c) 29.13.
(d) 41.15.
(e) None of the above.
9.
Are
the slope of the population regression line, B, and the slope of the sample
regression line, b, fixed parameters or are they random variables?
(a) B is a fixed parameter and b is a random
variable.
(b) B is a random variable and b is a fixed
parameter.
(c) Both B and b are fixed parameters.
(d) Both B and b are random variables.
(e) None of the above.
10.
If
the sample correlation coefficient (r) is 0.5, this means that
(a)
none
of the variation in the dependent variable is explained by the regression.
(b)
25
percent of the variation in the dependent variable is explained by the regression.
(c)
50
percent of the variation in the dependent variable is explained by the
regression.
(d)
75
percent of the variation in the dependent variable is explained by the
regression
(e)
none
of the above.
11.
If
the sample correlation coefficient is 0.4, this means that
(a)
the
dependent variable is inversely related to the independent variable.
(b)
the
dependent variable increases at an increasing rate with increases in the
independent variable.
(c)
the
dependent variable increases at a decreasing rate with increases in the independent
variable.
(d)
the
dependent variable is directly related (in the sample) to the independent
variable.
(e)
the
dependent variable is directly related (in the population) to the independent
variable.
12.
If
a hypothesis test rejects the null hypothesis (at a pre-specified level of
significance), that means:
(a)
The
null is proven to be false.
(b)
The
alternative is proven to be true.
(c)
The
null is shown to be more likely to be true than the alternative.
(d)
The
alternative is shown to be more likely to be true than the null, given the
sample evidence.
13.
While
testing for a null hypothesis, the chances of rejecting the null, every thing
else remaining the same, is more if one is working with the 5% rather than the
1% level of significance.
(a)
yes
(b)
no
(c)
depends
(d)
none
of the above
(a)
has
the least amount of bias.
(b)
has
a symmetric sampling distribution.
(c)
has
a sapling distribution whose mean is zero.
(d)
has
a sampling distribution whose variance is the least among all unbiased
estimators.
15.
(5
points) Suppose you are testing for the significance of the regression
coefficient B1 in Yi = A + B1.X1i +
B2.X2i + ei with a sample size of 100. In
looking up for the critical t value from the t table, what
degrees of freedom should you use at the 5% level of significance?
16.
(10
points) Suppose the relationship between Yi and Xi is
given by the following nonlinear regression:
Yi = a.Xib.zi
where a and b are the parameters we want to estimate, and
zi is the random error term.
Explain how, with your knowledge of linear least squares, you can estimate a and b.
17.
(10
points) If the sample correlation coefficient is 0.30 and sample size equals
20, test whether the population correlation coefficient is zero. (Let the level
of significance be 5% and use a two-tailed test.)
18.
(15
points) An economist at Albany International wants to estimate the relationship
between a worker’s productivity (Yi) a particular job, on the one
hand, and the worker’s sex (Hi) and score (Xi) an
aptitude test, on the other hand. She obtains data for 15 people, and
calculates the following regression:
Yi = A + 1.176 Xi + 9.90 Hi
Hi
is defined such that Hi equals zero if the worker is male, and 1 if
the worker is female.
Holding
the test score constant, what is the average difference in productivity between
a male and a female on this job?
If
a male scores 82 on the aptitude test, what would you estimate his productivity
to be?
If
a female scores 76 on the aptitude test, what would you estimate her
productivity to be?
19.
A
firm examines a random sample of 10 spot welds of steel. In each case, the
shear strength of the weld and the diameter of the weld are determined, the
results being as follows:
Shear Strength:
680, 800, 780, 885, 975, 1025, 1100, 1030, 1175, 1300
(Pounds)
Weld diameter:
190, 200, 209, 215, 215,
215, 230, 250,
265, 250
(Thousandths of an inch)
Based on the above data the following were obtained:
SX=2239; SY=9750; SX2=506,581; SY2=9,836,800; SXY=2,219,370
The means of X and Y were 223.9 and 975.0
respectively.
(a)
Calculate
the least squares estimates of A and B in a regression of shear strength on
weld diameter.
(b)
Compute
the standard error of estimate. What does this number mean?
(c)
Compute
the coefficient of determination. What does this number mean?
(d)
What
proportion of the variation in weld strength in the sample can be explained by
weld diameter?
(e)
Compute
the standard error of b.
(f)
Test
the null hypothesis that B = 0 against the alternative that it exceeds zero at
.01 significance level.
(g)
Test
the hypothesis that the correlation coefficient is zero using a two-tailed test
at the .05 significance level.
20.
What are Three techniques to explain economic relationship & difference among them; and what are three applications of statistics.
21.
What are assumptions of Linear Regression. What are Properties of OLS estimates in small samples and large samples, Explain the meaning of each property.
22.
Show how to estimate one of three nonlinear models.