URGENT PLEASE HELP

Question

There are many measurements of the human body that are positively correlated. For example, the length of one's forearm (measured from elbow to wrist) is approximately the same length as the foot (measured from heel to toe). They are positively correlated because, as one measurement increases, so does the other measurement. You will discover through this project whether a human's arm span (measured across the body with the arms extended) is correlated to his height.

You will need to collect data from 11 people, which will give you 12 data points including your own personal data. You will turn in and answer questions regarding only one scatter plot if doing the project alone. You may use the sample data provided in Part One if you do not have 11 people to measure. Part One: Measurements Measure your own height and arm span (from finger-tip to finger-tip) in inches. You will likely need some help from a parent, guardian, or sibling to get accurate measurements.

Record your measurements on the "Data Record" document. Use the "Data Record" to help you complete Part Two of this project. Measure 11 additional people, and record their arm spans and heights in inches. You may use the sample data provided in the table if you do not have 11 people to measure. Arm Span (inches) Height (inches) 58 60 49 47 51 55 19 25 37 39 44 45 47 49 36 35 41 40 46 50 58 61

Part Two: 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.

Part Three: 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 form of the line 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 Part Three,

Question 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?

Answer 1

PART TWO :

THE SCATTER PLOT OF THE DATA IS GIVEN BELOW

THE LINE OF BEST FIT IS ALSO WRITTEN ON GRAPH

2) a) I took 2 points from the graph (19.992, 24.679) and (37.842, 40.687)

b) slope is

m = (Y2 - Y1) / (X2 - X1) = (40.687 - 24.679) / (37.842 - 19.992) = 0.897

c) put (X1, Y1) = (19.992 , 24.679)

equation of the line is Y - Y1 = m( X - X1)

Y - 24.679 = 0.897 (X - 19.992)

d) When above equation expands it becomes

0.897 X - Y = - 6.746 or

Y = 0.897 X + 6.746 this is the slope intercept form

3) Here slope m represents the increment in height in inches with respect to unit inch increment in arm span. That means for every 1 inch increase in the arm span there is an increment of 0.897 inch in height. The y intercept is the height of the individual of those who have 0 inch arm span. By common sense it is absurd but mathematically in graph it is possible by extrapolation.

4) I took 2 points ( 27.132, 30.015) and (47.124, 51.359)

For first coordinate

Arm span = 27.132 inch

Height by equation = Y = 0.897 X + 6.746 = 0.897 x 27.132 + 6.746 = 31.083 inch

Actual height from graph = 30.015 inch

For second coordinate

Arm span = 47.124 inch

Height by equation = Y = 0.897 X + 6.746 = 0.897 x 47.124 + 6.746 = 49.016 inch

Actual height from graph = 51.359 inch

5) There is a slight error in the calculated values of height may due to the blurred graph provided. According to the equation the height is 0.897 times arm span plus 6.746 inches. So height is always greater than the arm span.

6) If the arm span of a tall person is X = 66 inches then

Height = Y = 0.897 X + 6.746 = 0.897 x 66 + 6.746 = 65.948 inches

7) if the height is Y = 74 inch

Then Y = 0.897 X + 6.746 or X = ( Y - 6.746) / 0.897

Arm span = X = (74 -6.746) / 0.897 = 74.97 inches

so the arm span is dominating over height from here on but actually in real world that is wrong. So for large arm span the graph is deviating from actual value in large extent.