NAME: ___________________________________________ REVIEW WORKSHEET ON CHAPTER 4
NAME: ___________________________________________ XXXXXXXXXXWORKSHEET # 3
Due __________________________
Fifteen females of varying ages were asked to keep a record of the number of phone calls made to family/friends during the course of a week. The results are given below:
age
13
20
52
38
29
64
16
60
58
40
24
89
35
18
44
calls
55
25
15
28
26
8
49
10
13
21
40
4
32
45
22
ANSWER THE FOLLOWING QUESTIONS FOR THE PROBLEM ABOVE.
USE THE COMPUTER PRINTOUT PROVIDED TO CHECK YOUR ANSWERS.
1. Which of the following is true about the two variables?
a. The age of the woman is the explanatory variable and the number of calls is the response variable.
. The number of calls is the explanatory variable and the age of the woman is the response variable.
c. It is not possible to tell which variable is explanatory and which is response.
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2. How many pieces of data are there in the data set?
a. 15
. 30
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3. Draw a scatter plot. Be sure to label both axes.
XXXXXXXXXX_________________________________________________________________________
4. The relationship between the two variables is:
a. positive
. negative
c. cannot be determined
5. This means that:
a. younger women make fewer phone calls per week
. older women make fewer phone calls per week
c. older women make more phone calls per week
6. Find the values for Sxx, Syy, and Sxy. Show all work.
x
y
x2
y2
xy
XXXXXXXXXXwork for Sxx
XXXXXXXXXXwork for Syy
XXXXXXXXXXwork for Sxy
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Give the three values here:
Sxx = __________________
Syy = __________________
Sxy = __________________
7. How strong is the linear relationship between the age of the female and the number of calls per week?
To answer this question, which variable should be calculated?
a. slope
b. y-intercept
XXXXXXXXXXc. co
elation coefficient
d. coefficient of determination
Calculate this value. Show all work.
Interpret the meaning of this value in terms of the problem.
8. Find the least squares regression line. Use the formulas and show the work. Compare with the printout.
slope
y-intercept
XXXXXXXXXXequation
9. Interpret the slope and y-intercept of the line in terms of the problem.
slope
y-intercept
10. How well does the regression line found in #8 fit the data?
XXXXXXXXXXTo answer this question, which variable should be calculated?
a. slope
b. y-intercept
c. co
elation coefficient
XXXXXXXXXXd. coefficient of determination
XXXXXXXXXXCalculate this value. Show all work.
Interpret the meaning of this value in terms of the problem.
(There are 2 parts to this interpretation.)
11. Calculate the residual by hand for a 38 year old female.
XXXXXXXXXXShow all work, label the answer, and check your results with the printout.
12. Estimate the number of calls made per week by a female who is: (Show all work; label answers.)
a. 42 years old
. 8 years old
13. Can it be concluded from these calculations that the age of a female has an effect on the
XXXXXXXXXXnumber of calls made per week? Explain thoroughly.
ROW
age
calls
predcall
resid
1
13
55
43.7776
11.2224
XXXXXXXXXX20
25
XXXXXXXXXX.2204
3
52
15
18.3877
XXXXXXXXXX
XXXXXXXXXX38
28
27.5020
XXXXXXXXXX
XXXXXXXXXX29
26
33.3612
XXXXXXXXXX
XXXXXXXXXX64
8
10.5755
XXXXXXXXXX
XXXXXXXXXX16
49
41.8245
XXXXXXXXXX
XXXXXXXXXX60
10
XXXXXXXXXX3.1796
XXXXXXXXXX58
13
14.4816
XXXXXXXXXX
XXXXXXXXXX40
21
26.2000
XXXXXXXXXX
11
24
40
36.6164
XXXXXXXXXX
12
89
4
XXXXXXXXXX
XXXXXXXXXX
13
35
32
29.4551
XXXXXXXXXX
14
18
45
40.5225
XXXXXXXXXX
15
44
22
23.5959
XXXXXXXXXX
The regression equation is
calls = 52.2 – 0.651 age
Predicto
Coef
Stdev
t-ratio
p
Constant
XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX
age
XXXXXXXXXX0. XXXXXXXXXX XXXXXXXXXX.54
XXXXXXXXXX
s = 6.940 XXXXXXXXXXR-sq = 81.4% XXXXXXXXXXR-sq (adj) = 79.9%
Analysis of Variance
SOURCE
DF
SS
MS
F
p
Regression XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX
E
o
XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX48.2
Total
14
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