Mathematics, 07.07.2020 20:01 kaydrama2003

Arm Span(x) Height(y) (58, 60)
(49, 47)
(51, 55)
(19, 25)
(37, 39)
(44, 45)
(47, 49)
(36, 35)
(41, 40)
(46, 50)
(58, 61)
(67, 63)

1. Representation of Data with Plots Using graphing software of your choice, create a scatter plot of your data. Predict the line of best fit, and sketch it on your graph. Copy and paste your scatter plot into a word processing document.

2. The Line of Best Fit Include your scatter plot and the answers to the following questions in your word processing document:

Which variable did you plot on the x-axis, and which variable did you plot on the y-axis? Explain why you assigned the variables in that way.

Write the equation of the line of best fit using the slope-intercept formula y = mx + b. Show all your work, including the points used to determine the slope and how the equation was determined.

What does the slope of the line represent within the context of your graph? What does the y-intercept represent?

Test the residuals of two other points to determine how well the line of best fit models the data. Use the line of best fit to help you to describe the data correlation.

Using the line of best fit that you found in 2, approximate how tall is a person whose arm span is 66 inches?

According to your line of best fit, what is the arm span of a 74-inch-tall person?

Arm Span(x) Height(y)

(58, 60) (49, 47) (51, 55) (19, 25) (37, 39) (44, 45) (47, 49) (36,

Answers: 3

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Answers

Answer from: babygirlqueen5588

Here's what I get.

Step-by-step explanation:

1. Representation of data

I used Excel to create a scatterplot of the data, draw the line of best fit, and print the regression equation.

2. Line of best fit

(a) Variables

I chose arm span as the dependent variable (y-axis) and height as the independent variable (x-axis).

It seems to me that arm span depends on your height rather than the other way around.

(b) Regression equation

The calculation is easy but tedious, so I asked Excel to do it.

For the equation y = ax + b, the formulas are

$a = \dfrac{\sum y \sum x^{2} - \sum x \sumxy}{n\sum x^{2}- \left (\sum x\right )^{2}}\\\\b = \dfrac{n\sumx y - \sum x \sumxy}{n\sum x^{2}- \left (\sum x\right )^{2}}$

This gave the regression equation:

y = 1.0595x - 4.1524

The line shows how arm span depends on height.

The slope of the line says that arm span increases about 6 % faster than height.

The y-intercept is -4. If your height is zero, your arm length is -4 in (both are impossible).

(d) Residuals

$\begin{array}{cccr}&\textbf{Arm Span} & \textbf{Arm Span}&\\\textbf{Height/in} &\textbf{Actual} & \textbf{Predicted}&\textbf{Residual}\\25 & 19 & 22.3 & -3.3\\40 & 41 & 38.2 & 2.8\\55 & 51 & 54.1 & -3.1\\65 & 67 & 62.6 & 4.4\\ \end{array}$

The residuals appear to be evenly distributed above and below the predicted values.

A graph of all the residuals confirms this observation.

The equation usually predicts arm span to within 4 in.

(e) Predictions

(i) Height of person with 66 in arm span

$\begin{array}{rcl}y& = & 1.0595x - 4.1524\\66 & = & 1.0595x - 4.1524\\70.1524 & = & 1.0595x\\x & = & \dfrac{70.1524}{1.0595}\\\\& = & \textbf{66 in}\\\end{array}\\\text{A person with an arm span of 66 in should have a height of about $\large \boxed{\textbf{66 in}}$}$

(ii) Arm span of 74 in tall person

$\begin{array}{rcl}y& = & 1.0595x - 4.1524\\& = & 1.0595\times74 - 4.1524\\& = & 78.4030 - 4.1524\\& = & \textbf{74 in}\\\end{array}\\\text{ A person who is 74 in tall should have an arm span of $\large \boxed{\textbf{74 in}}$}$

Arm Span(x) Height(y)

(58, 60) (49, 47) (51, 55) (19, 25) (37, 39) (44, 45) (47, 49) (36, 35

Answer from: Quest

c. x=2.4cm

step-by-step explanation:

similar triangles are triangles which have the same shape but not the same size. this means their angle measures are equal but their side lengths are not instead they are proportional. to solve, we will set up a proportion and solve.

a proportion is two equal ratios set equal to each other. we form the ratios by finding corresponding sides (sides which match to each other on both triangles by their position). out ratios will be one side of the small triangle over the corresponding side on the big triangle as shown below:

$\frac{little}{big} =\frac{side mn}{side ab}=\frac{side on}{side cb}$ .