Question
In: Statistics and Probability
The table lists heights (in.) of fathers and the heights (in.) of their first sons. Height...
The table lists heights (in.) of fathers and the heights (in.) of their first sons.
|
Height of father (x) |
73.0 |
75.5 |
75.0 |
75.0 |
75.0 |
74.0 |
74.0 |
73.0 |
73.0 |
78.5 |
|
Height of first son (y) |
74.0 |
73.5 |
71.0 |
70.5 |
72.0 |
76.5 |
74.0 |
71.0 |
72.0 |
73.2 |
- Find the linear correlation coefficient r
- Predict the height of a father whose first son measures 77 in.
Solutions
Expert Solution
Solution:
| X | Y | XY | X^2 | Y^2 |
| 73 | 74 | 5402 | 5329 | 5476 |
| 75.5 | 73.5 | 5549.25 | 5700.25 | 5402.25 |
| 75 | 71 | 5325 | 5625 | 5041 |
| 75 | 70.5 | 5287.5 | 5625 | 4970.25 |
| 75 | 72 | 5400 | 5625 | 5184 |
| 74 | 76.5 | 5661 | 5476 | 5852.25 |
| 74 | 74 | 5476 | 5476 | 5476 |
| 73 | 71 | 5183 | 5329 | 5041 |
| 73 | 72 | 5256 | 5329 | 5184 |
| 78.5 | 73.2 | 5746.2 | 6162.25 | 5358.24 |
| n | 10 |
| sum(XY) | 54285.95 |
| sum(X) | 746.00 |
| sum(Y) | 727.70 |
| sum(X^2) | 55676.50 |
| sum(Y^2) | 52984.99 |
| Numerator | -4.70 |
| Denominator | 274.50 |
| r | -0.0171 |
| r square | 0.0003 |
| Xbar(mean) | 74.6000 |
| Ybar(mean) | 72.7700 |
| SD(X) | 0.8375 |
| SD(Y) | 2.0293 |
| b | -0.0189 |
| a | 74.1781 |
a)
r = -0.0171
The linear correlation coefficient r = -0.0171
b)
b = -0.0189
a = 74.1781
So , the equation of the regression line is
= a + bx
= 74.1781 + (-0.0189)x
Put x = 77 in this equation.
= 74.1781 + [(-0.0189)* 77]
= 72.7228 inches
orchestra answered 1 year agoRelated Solutions
The following data are the heights of fathers and their sons in inches. The father's height...
The following data are the heights of fathers and their sons in
inches. The father's height is his height when he was the same age
as the son.
Father's Height
Son's Height
44
44
47
47
43
46
41
42
45
47
44
44
44
45
44
45
a. A geneticist might wonder if there is a tendency for tall
fathers to have tall sons and short fathers to have short sons.
Answer this question by computing the appropriate statistic...
Heights of Fathers and their sons Fathers Sons 6'0 5'9 5'11 6'1 5'11 5'11 6'1...
Heights of Fathers and their sons
Fathers Sons
6'0 5'9
5'11 6'1
5'11 5'11
6'1 5'9
5'9 5'7
6'2 5'10
6'0 6'0
6'1 5'11
5'8 5'11
5'11 6'2
Clearly organize your data in a table and
graph it in a scatter plot (this can be hand
written).
Test to see if there is a linear correlation
between the variables x and y (father height and son height) by
finding the linear correlation coefficient r. (use a 0.05
significance level)...
An anthropologist records the heights (in inches) of ten fathers and their sons. Use the Spearman...
An anthropologist records the heights (in inches) of ten fathers
and their sons. Use the Spearman rank correlation test to analyze
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Heights
Son's Height
Father's Height
64
64
57
66
52
79
50
78
41
77
40
90
66
81
78
80
58
61
56
82
Step 1 of 2:
Find the value of the correlation coefficient to test for an
association between the heights of the fathers and the heights of
their sons. Round your answer to...
A researcher randomly selects 6 fathers who have adult sons and records the fathers' and sons'...
A researcher randomly selects 6 fathers who have adult sons and
records the fathers' and sons' heights to obtain the data shown
in the table below. Test the claim that sons are taller than their
fathers at the alpha equals 0.10α=0.10 level of significance. The
normal probability plot and boxplot indicate that the differences
are approximately normally distributed with no outliers so the use
of a paired t-test is reasonable
67.5
72.9
68.4
71.2
67.7
66.8
71.1
71.3
67.6
74.7...
A researcher randomly selects 6 fathers who have adult sons and records the fathers' and sons'...
A researcher randomly selects 6 fathers who have adult sons and
records the fathers' and sons' heights to obtain the data shown
in the table below. Test the claim that sons are taller than their
fathers at the
α=0.10
level of significance. The normal probability plot and boxplot
indicate that the differences are approximately normally
distributed with no outliers so the use of a paired t-test is
reasonable.
Observation
1
2
3
4
5
6
Height of father (in inches)...
The table lists height (in) and weights (lb) of randomly selected 8 students. Height (in) 60...
The table lists height (in) and weights (lb) of randomly
selected 8 students.
Height (in) 60 65 66 68 60 67 69 70
Weight (lb) 150 152 156 160 160 167 168 170
(a) Find the the value of coefficient of correlation r.
(b) Find the equation of the line of best best fit (trend line).
What does variable y represents?
(c) Estimate weight of a student from the same group who is 64
inches tall.
The following table lists the activities needed to complete a project. The first column lists the...
The following table lists the activities needed to complete a
project. The first column lists the activities and the “follows”
column shows which other activity or activities, (if any), must be
completed before these activities can start. The remaining columns
give three estimates of the activity duration; the mean duration
calculated from these estimates and standard deviation assuming a
beta distribution of activity duration.
Activity
Follows
Estimates of durations (days)
Optimistic
Most likely
Pessimistic
A
--
3
6
15
B...
The following table lists the activities needed to complete a project. The first column lists the...
The following table lists the activities needed to complete a
project. The first column lists the activities and the “follows”
column shows which other activity or activities, (if any), must be
completed before these activities can start. The remaining columns
give three estimates of the activity duration; the mean duration
calculated from these estimates and standard deviation assuming a
beta distribution of activity duration.
Activity
Follows
Estimates of durations (days)
Optimistic
Most likely
Pessimistic
A
--
3
6
15
B...
To test the belief that sons are taller than their fathers, a student randomly selects 13...
To test the belief that sons are taller than their fathers, a
student randomly selects 13 fathers who have adult male children.
She records the height of both the father and son in inches and
obtains the following data. Note: A normal probability plot and
boxplot of the data indicate that the differences are approximately
normally distributed with no outliers
Height of
Father,71.9,71.8,68.5,73.2,70.9,69.8,69.3,72.3,71.9,70.2,69.8,69.8,69.1
Xi Height of Son, Yi 76.8, 75.2, 71.0, 75.0, 72.0, 70.3, 69.4,
71.7, 70.6, 68.4, 67.3, 66.3,...
To test the belief that sons are taller than their fathers, a student randomly selects 6...
To test the belief that sons are taller than their fathers, a
student randomly selects 6 fathers who have adult male children.
She records the height of both the father and son in inches and
obtains the accompanying data. Are sons taller than their fathers?
Use the alpha equals 0.1 level of significance. Note that a normal
probability plot and boxplot of the data indicate that the
differences are approximately normally distributed with no
outliers.
Observation
1
2
3
4...
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