Question

How strongly do physical characteristics of sisters and brothers correlate? Here are data on the heights (in inches) of 12 adult pairs:

Brother 71 68 66 67 70 71 70 73 72 65 66 70

Sister 69 64 65 63 65 62 65 64 66 59 62 64

a. Use your calculator or software to find the correlation and the equation of the least-squares line for predicting sister’s height from brother’s height. Make a scatterplot of the data, and add the regression line to your plot.

b. Damien is 70 inches tall. Predict the height of his sister Tonya. Based on the scatterplot and the correlation r, do you expect your prediction to be very accurate? Why?

Answer #1

x= Brother , y= sister

x | y | xy | x2 | y2 | |

71 | 69 | 4899 | 5041 | 4761 | |

68 | 64 | 4352 | 4624 | 4096 | |

66 | 65 | 4290 | 4356 | 4225 | |

67 | 63 | 4221 | 4489 | 3969 | |

70 | 65 | 4550 | 4900 | 4225 | |

71 | 62 | 4402 | 5041 | 3844 | |

70 | 65 | 4550 | 4900 | 4225 | |

73 | 64 | 4672 | 5329 | 4096 | |

72 | 66 | 4752 | 5184 | 4356 | |

65 | 59 | 3835 | 4225 | 3481 | |

66 | 62 | 4092 | 4356 | 3844 | |

70 | 64 | 4480 | 4900 | 4096 | |

829 | 768 | 53095 | 57345 | 49218 | Total |

69.08333 | 64 | Average |

**Correlation(r) = 0.55463 (**use Excel function
=Correl(xarray, yarray) i.e
=correl(A2:A13,B2:B13)**)**

**Y= 0.5206x + 28.037**

**b) x = 70**

**Y= 0.5206*70 + 28.037 = 64.479.**

**It is not very accurate because of r, the value of r is
<0.7 which show not highly correlated**

How strongly do physical characteristics of sisters and brothers
correlate? The data in the table give the heights (in inches) of
1212 adult pairs.
Brother
7171
6868
6666
6767
7070
7171
7070
7373
7272
6565
6666
7070
Sister
6969
6464
6565
6363
6565
6262
6565
6464
6666
5959
6262
6464
Enter the equation of the least‑squares regression line, with
the numerical values rounded to three decimal places and xx as the
explanatory variable.
^y=
Assume Damien is 6767 inches tall....

A randomly selected sample of college basketball players has the
following heights in inches.
65, 63, 67, 67, 67, 70, 63, 65, 62, 66, 70, 62, 68, 67, 69, 67,
61, 68, 67, 67, 64, 69, 67, 62, 63, 65, 63, 65, 71, 62, 64, 61
Compute a 95% confidence interval for the population mean height
of college basketball players based on this sample and fill in the
blanks appropriately.
___ < μ < ___ (Keep 3 decimal places)

DaughtersHeight.sav is a data set on the height of
adult daughters and the heights of their mothers and fathers, all
in inches. The data were extracted from the US Department of Health
and Human Services, Third National Health and Nutrition Examination
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data on the heights of 37 randomly selected female engineering
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62 64 61 67 65 68 61 65 60 65 64 63 59
68 64 66 68 69 65 67 62 66 68 67 66 65
69 65 69 65 67 67 65 63 64 67 65
We found that the sample mean and sample standard deviation for
this sample data are 65.16 inches and 2.54 inches, respectively. Do
you find sufficient evidence in the sample data...

Do this one by hand. Suppose we measured the height of
10,000 men and found that the data were normally
distributed with a mean of 70.0 inches and a
standard deviation of 4.0 inches. Answer the
questions and show your work:
A. What
proportion of men can be expected to have heights less
than: 66, 70, 72, 75 inches?
B. What
proportion of men can be expected to have heights greater
than: 64, 66, 73, 78 inches?
C. What
proportion...

The accompanying frequency table shows the heights? (in inches)
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deviation. c right parenthesis Display these data with a histogram.
d right parenthesis Write a few sentences describing the
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members. ?
Height Count
60 1
61 6
62 10
63 6
64 3
65 20
66 19
67...

22) Given the paired data set below of Super Models
heights and weights, then Determine the Line of Regression.
X |
65 67 62
68 66 69
61 67 64 69
Y | 110 105 113 107 109 111
104 110 116 115
23) Calculate the Coefficient of Correlation for the
data of problem 22
24) Using the Line of Regression from problem 22,
predict the weight of a Model who is 69 inches tall.
25) Using the data from problem 22 construct a
Scatter...

The following data values represent a sample of
the heights of female college basketball players. SHOW WORK.
Heights in Inches
65 66 66 67 68 68 68 69 69 69 69 70 71
72 72 72 73 75 75 75 75 76 76 76 76
a) Determine (to two decimal places) the mean height and sample
standard deviation of the heights.
b) Determine the z-score of the data value X = 75 to the
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c) Using results from...

1. (20 pts) Do this one by
hand. Suppose we measured the height of 5,000 men
and found that the data were normally distributed with a
mean of 70.0 inches and a standard
deviation of 4.0 inches. Answer the questions using Table
A and show your work:
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Perform a Spearman Rank Correlation Coefficient Test at a
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Height (in.)
Foot Length (in.)
63
10
66
12
62.5
9.4
74
10.5
70
11.3
72
11.3
71
12.5
64
9.1
72
10.9
71
10
74
12.1
67
10
69
11.1
65
9.6
62.8
9
72
11.3
68.8
10.5
69
10
65.3
9
53
7
71
10.3
74
11.7
70
10
72
10.6
72.5
12.8
67
9.5
69
10.9
74
11.6
68
9...

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