How strongly do physical characteristics of sisters and brothers correlate? The data in the table give the heights (in inches) of 1212 adult pairs.Brother717168686666676770707171707073737272656566667070Sister696964646565636365656262656564646666595962626464To access the data, click the link for your preferred software format. CSV Excel (xls) Excel (xlsx) JMP Mac-Text Minitab14-18 Minitab18+ PC-Text R SPSS TI CrunchIt! © Macmillan LearningAssume Damien is 6767 inches tall. Predict the height of his sister Tonya. Give your answer to one decimal place.Tonya's predicted height:

The given data is as follows. Brother Sister 71 69 68 64 66 65 67 63 70 65 71 62…

Answered: How strongly do physical…

Holt Mcdougal Larson Pre-algebra: Student Edition 2012

1st Edition

ISBN:9780547587776

Author:HOLT MCDOUGAL

Publisher:HOLT MCDOUGAL

Chapter12: Angle Relationships And Transformations

Section12.1: Angle Relationships

Problem 44E

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Question

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

To access the data, click the link for your preferred software format.

CSV Excel (xls) Excel (xlsx) JMP Mac-Text Minitab14-18 Minitab18+ PC-Text R SPSS TI CrunchIt!

Assume Damien is 6767 inches tall. Predict the height of his sister Tonya. Give your answer to one decimal place.

Tonya's predicted height:

Expert Solution

Step 1

The given data is as follows.

Brother	Sister
71	69
68	64
66	65
67	63
70	65
71	62
70	65
73	64
72	66
65	59
66	62
70	64

The random variable $X$ is brothers' height.

The random variable $Y$ is sisters' height.

The formula for the correlation coefficient is as follows.

$r = \frac{\sum_{i = 1}^{n} (x_{i} - x) (y_{i} - y)}{\sqrt{\sum_{i = 1}^{n} {(x_{i} - x)}^{2} \sum_{i = 1}^{n} {(y_{i} - y)}^{2}}}$

$x$ is the sample mean of sample one.

$y$ is the sample mean of sample two.

$n$ is the sample size.

The simple linear regression line is as follows

$y = a + b x$

$y$ is the dependent variable.

$x$ is independent variable

$b = \frac{\sum_{i = 1}^{n} (x_{i} - x) (y_{i} - y)}{\sum_{i = 1}^{n} {(x_{i} - x)}^{2}} a = y - b x$

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Enter the equation of the least‑squares regression line, with the numerical values rounded to three decimal places and ?� as the explanatory variable. (If you are using CrunchIt, adjust the default precision under Preferences as necessary.

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