MGMT2263
Worksheet #6
An educational researcher wanted to see what factors influenced school grades and examined the average number of hours students studied for a test, average number of hours of sleep per night, gender and household income level. For the purposes of doing regression, male=0 and female=1 and low income = 0 and medium/high income = 1. Twenty subjects were randomly chosen. These were the results:
|
grade |
study |
sleep |
gender |
income |
|
71 |
4 |
6 |
0 |
0 |
|
75 |
3 |
9 |
0 |
0 |
|
61 |
6 |
7 |
1 |
0 |
|
63 |
8 |
6 |
1 |
1 |
|
63 |
6 |
10 |
0 |
0 |
|
58 |
7 |
7 |
1 |
0 |
|
60 |
5 |
9 |
1 |
0 |
|
90 |
10 |
7 |
0 |
0 |
|
93 |
9 |
10 |
1 |
0 |
|
83 |
11 |
8 |
0 |
1 |
|
73 |
9 |
5 |
0 |
1 |
|
75 |
12 |
6 |
0 |
0 |
|
87 |
12 |
5 |
0 |
1 |
|
88 |
12 |
4 |
1 |
0 |
|
90 |
14 |
6 |
0 |
0 |
|
47 |
4 |
4 |
1 |
0 |
|
98 |
11 |
8 |
1 |
1 |
|
96 |
11 |
10 |
1 |
0 |
|
64 |
7 |
7 |
1 |
1 |
|
45 |
5 |
6 |
1 |
1 |
1)
Construct
a model with grade as the dependent variable and the other variables as the
independent variables. State what the model is (grade = 24.3923 + 3.8911*study
+ 2.9052*sleep – 3.8384*gender – 2.6087*income)
2)
What
percentage of the variation in grade is explained by the model? (70.16%)
3)
Is
the model significant? (F = 8.8164; yes, the model is significant)
4)
What
individual variables are significant? (study and sleep; these are the only
variables in which the p-value is less than 5%)
5)
Are
there any collinearity problems among the independent variables? (no – all the
VIF values are less than 10)
6)
Construct
a new model using only study and sleep as the independent variables. State what
the model is. (grade = 20.0198 + 3.9576*study + 3.0188*sleep)
7)
If
someone studies for 10 hours on average and sleeps for 7 hours, what would you
expect the person’s grade to be, rounding to the nearest whole number? (81)
8)
Based
on 10 hours of study and 7 hours of sleep, in what grade range would you expect
the average grade to fall 95% of the time, rounding to the nearest whole
number? (76 to 86)
9)
For
an individual who studies for 10 hours and sleeps for 7 hours, in what grade
range would you expect the person’s grade to fall 95% of the time? (60 to 100
since the mark cannot be above 100)
10)
Using
the criteria of adjusted r2, ANOVA p-value and t-test p-values
(using a 5% level of significance), which of the two models is best? (Model #2)
A family resource centre
wanted to see if a client’s age depends on their gender. These were the results
for one particular day:
|
|
Child |
Adolescent |
Adult |
Total |
|
Male |
24 |
9 |
12 |
45 |
|
Female |
30 |
15 |
20 |
65 |
|
Total |
54 |
24 |
32 |
110 |
11) Test the
hypothesis at 5%. (test stat = 0.548; conclude age does not depend on gender)
12) To what
degree does a person’s age depend on their gender? (7.06%)
A non-profit organization
wanted to see if the number of volunteer hours depended on a person’s work
status. These were the results:
|
Contingency
Table |
||||
|
|
Hours
group |
|
||
|
Group |
< 10 |
10 to 19 |
20+ |
Grand
Total |
|
Working |
10 |
4 |
0 |
14 |
|
Semi-retired |
13 |
23 |
2 |
38 |
|
Retired |
15 |
30 |
8 |
53 |
|
Grand
Total |
38 |
57 |
10 |
105 |
13) Which
categories need to be collapsed? (10 to 19 hours and 20+ hours)
14) After
collapsing categories, test the hypothesis at 5%. (test stat = 9.019; conclude
the number of volunteer hours depends on a person’s work status)
15) To what
degree does the number of hours depend on a person’s work status? (29.31%)
In
a survey at a mall during August, people were asked how much they spent that
day. For a sample of 8 people these were the results:
|
50 |
75 |
100 |
120 |
140 |
150 |
240 |
1350 |
16) Is the data normally distributed? Test at a 5% level of significance. (test stat = 0.4109; data is not normally distributed)
17) Clearly 1350 is an outlier. If we remove this value, show why the remaining data is normally distributed.