# SOLUTION: De Anza College Gross Domestic Product and Life Expectancy Questions

Lecture 22
Find the equation of the lowest squares retrogression row for the abandoned postulates.
(a) The caloric pleased and the sodium pleased (in milligrams) for 10 beef hot dogs.
1.
Calories, x
Sodium, y
Answer:
150
420
170
470
120
350
120
360
90
270
180
550
170
530
140
460
90
380
110
330
^ = 2.472x + 80.813
y
(b) The apex (in feet) and stem transections (in inches) of 11 trees.
Height, x
Trunk transection,
Answer:
y
70
8.3
72
10.5
75
11.0
76
11.4
71
9.2
73
10.9
85
14.9
78
14.0
77
16.3
80
18.0
82
15.8
^ = 0.560x -29.922
y
The postulates in the board represents per capita Gross Domestic Product (GDP), in thousands of
dollars, of ten randomly selected Western European countries and the identical conduct wait-forancy
(in years) of their population.
2.
Country
Austria
Belgium
Finland
France
Germany
Ireland
Italy
Netherlands
Switzerland
United Kingdom
Per Capita GDP(thousands of dollars)
21.4
23.2
20.0
22.7
20.8
18.6
21.5
22.0
23.8
21.2
Life Trust (in years)
77.48
77.53
77.32
78.63
77.17
76.39
78.51
78.15
78.99
77.37
(a) Is it dispassionate to wait-for a cause-and-e ect correlativeness betwixt conduct wait-forancy and GDP?
Explain.
(b) Which of the two capriciouss is the vindication capricious? Explain.
(c) Produce a disseminate contrive of the postulates and illustrate on its power, outline, and devise. (Read
the size for the de nitions of power, outoutdirection and devise.)
(d) Suppose an eleventh province is added to the list: Greece. Greece's GDP and conduct wait-forancy
are 13,900 dollars and 78.44 years, respectively. Incorporate Greece in the disseminate contrive of keep-akeep-apart (c).
What do you observe? Comment. (12.2.5)
3. For the GDP and conduct wait-forancy postulates, the emerge and the y -intercept for the equation of best- t
are 0.42 and 68.715, respectively. Greece is extreme from the computations.
(a) Write the equation of the best t-line.
(b) In normal mathematics courses, the emerge of a row is repeatedly understanded as: `the vary in the y
outdirection disjoined by the vary in the `x' outline'. An repeatedly used short-cut for this is rise/run.
The emerge of a retrogression row is to mathematically understanded in a homogeneous way. However, in
statistics, any understandations are to be executed among the `context of the completion at influence '. In light
of this, how would you understand 0.42?
(c) How would you understand the aim of the y -intercept? (12.4.1)
(a) For the GDP and conduct wait-forancy postulates, abuse the predicted y for each appraise of x.
(b) Abuse the hallucination associated delay each of the premonstrations. (12.4.5, 12.4.6)
4.
An economist is conducting elaboration encircling the savings manners of American families. A random
sample of ten families yields the aftercited (all quantities are in thousands of dollars):
5.
X
Y
= annual income
= annual savings
16
1.2
22
2.2
18
2.0
12
1.3
1
12
0.8
34
3.0
21
0.6
50
4.0
48
4.0
28
2.0
The aftercited statistics are abused:
s
x
= 13.844
s
y
= 1.222
= 26:1
x
= 2.11
y
r
= 0.924
(a) Produce a disseminate contrive of the postulates.
(b) Write the equation of the lowest-squares retrogression row. Answer: y^ = 0.0816x -0.0187
(c) Predict y for x = 25. What does this premonstration average?
(d) Predict y for x = 100. What does this premonstration average? Do you consider this premonstration?
Explain. (12.P.6)
2
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