Problem
Set 4
Due
March 18, 2004
1. Corporate social responsibility correlations. The data in Table 1 come
from Report on Business,
March 2004, pp.46-47, inserted in The Globe and Mail of February 27, 2004.
a. Choose one pair
of indicator variables (COMM to HR) for which you anticipate a high correlation
between the two variables and one pair for which you anticipate a smaller
correlation. Obtain the Spearman rank
correlation coefficient for each pair and test for significance. (See section 11.4.6, pp. 819-821 of chapter
11 of my text for the formulas). Show
calculations for computation of one of the Spearman correlation coefficients
and the associated t-test. Using the
ranks from one pair, obtain the Pearson correlation coefficient for the
ranks. Compare with the Spearman
correlation.
b. Two
commentators on corporate social responsibility argue in opposite directions
one claims that larger corporations can afford to be more socially responsible
while the other argues that smaller corporations need to be more socially
responsible in order to establish a more positive image. By examining correlations between TOTAL and
(i) employment, and (ii) revenues, is there evidence for either of these
claims?
c. Write
a short note summarizing the results of a. and b. and any other observations
you have on these data.
COMPANY
REV EMP TOT COMM GOVERN CUSTOMER EMPLOYEE ENVIRON HR
H-P
1.8 -- 75
69 71 63 77 83
69
Siemens
3.1 6.6 66
56 76 47 55 82
53
Nortel
10.6 37.0 61
78 71 50 61 59
45
Xerox
1.3 4.0 61
88 50 67 58 67
32
Celestica
8.3 38.0 52
56 62 50 53 52
24
GE
3.4 7.0 48
52 59 34 49 45
40
Bombardier
23.8 80.0 44
56 54 50 37 43
34
Rogers
2.0 4.1 42
39 52 52 48 32
27
ATI
1.4 2.3 39
22 45 50 45 31
41
Key:
Rev
corporate revenue in billions of dollars
Emp
employment in thousands
Tot
overall responsibility score
Comm
community and society
Govern
corporate governance
Customer
customers
Employee
employees
Environ
environment
HR
human rights
2. Explaining wage differences. The data in Table 2 are from a random sample
of full-time, full-year Saskatchewan employees, surveyed by Statistics Canada
in the Survey of Labour and Income
Dynamics. Survey data were obtained
in 2001 and refer to respondents income and labour force activity during the
2000 calendar year. This question asks
you to obtain regression equations with wages and salaries (WAGES) as the
independent variable and years of education (EDYRS) as the independent
variable.
a. Draw the scatter diagram with WAGES on the
vertical axis and EDYRS on the horizontal axis.
b. One argument presented in models of human capital is that increased education is associated with increased wages and salaries. In order to test this contention and obtain an estimate of the effect of education on wages and salaries, calculate the regression equation relating WAGES, as the dependent variable, to EDYRS as the independent variable. Also calculate the standard error of estimate, the standard deviation of the slope of the line, and R-squared. Also conduct a test for statistical significance of the line. Show your calculations and describe your findings in words.
c. On the
diagram of a., draw the line estimated in b. and the bands representing a
distance of one standard error on each side of the line. What proportion of individuals are within
one standard error of the line? Within
two standard errors?
d. A group of individuals completing
doctorates, each having spent eight years in graduate school, following
four-year undergraduate degrees, have salary offers ranging from $45,000 to
$75,000, with an average of $55,000.
Those at the lower end of the spectrum consider this range unfair,
arguing they have just as many years of education as those offered higher
salaries. Using information from this
sample, what might you say to them?
e. Someone claims that the female (id 16) who
is paid $60,000, but has only 13 years of education, is being paid more than
she deserves. Using information from
this sample, what might you comment about this claim?
f. From the regression equation, what is the
expected increase in wages and salary for the female id 5, if she obtains a
university degree? Would you have any
hesitation in recommending this course of action to her?
g. Comment on any difficulties you observe with
these data, including any observations you might have about possible violation
of assumptions (see Lewis-Beck, p. 26).
3. Use the data is Table 2 to obtain a regression equation
with wages and salaries as the dependent variable and two or more explanatory
variables. Attempt to improve the fit
of the regression equation over that of question 2. Explain your results.
Table 2.
Data from a random sample of twenty Saskatchewan respondents, SLID 2000
(Person File)
ID AGE SEX HOURS EXP
WAGES TINCOME EDYRS
1 40 2
1955 22 55000 55000 20.0
2 41 1
2448 21 55000 58800 14.0
3 41 1
2086 22 23000 23300 12.0
4 43 1
1926 21 39000 42475 12.5
5 41 2
2439 2 5250 6650
12.5
6 43 2
2086 22 27000 27350 12.0
7 37 2
1981 16 15500 16800 12.0
8 35 1
1945 14 60000 60000 16.5
9 46 2
2086 7 11500 13250 12.0
10 57 2
1564 36 22000 24400 10.0
11 41 2
2086 8 57500 57500 12.0
12 51 2
2086 97 49000 50000 15.1
13 30 1
2086 5 45000 45000 20.0
14 36 2
1825 13 23000 23000 12.0
15 57 1
1955 35 60000 65500 17.5
16 45 2
1825 31 60000 60000 13.0
17 30 2
1929 11 25000 25025 12.5
18 54
1 1564 97
12000 12050 11.0
19 26 2
1955 5 35000 35650 15.0
20 37 2
2086 18 22000 22000 13.0
Key:
ID
identification number of respondent
Age
age of respondent in years
Sex
sex of respondent: 1 = male, 2 = female
Hours
hours of paid work, 2000
Exp
years of experience in full-time, full-year equivalents, since respondent
first worked full-time
Wages
wage or salary in dollars, 2000
Tincome
total income of respondent in dollars, before taxes, 2000
Edyrs
years of education of respondent, full-time equivalent