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 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 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?

1. We plotted the arm span in the x-axis because the arm span is the independent variable that we are using the calculate how tall is a person based on their arm span. I plotted the person's height in the y-axis because the persons's height is a dependent variable; after all, we are estimating how tall a person is based on their arm span.

We can conclude that:

The x-axis represent the arm span because that is the independent variable.

The y-axis represent how tall a person is based on his arm span because the persons height depends on the arm span.

2. From our picture we can infer that our point are: (24,51),(24,56) (25,53), (25,54), (26,55), (26,56), (27,54), (29,55),(29,58), (30,59), and (33,61).

From our picture we can infer that the point that appear to be co-linear are: (25,53), (26,54), (29,58), and (30,59). We are going to use the end points (25,53) and (30,59) to create our lineal model. To do it, we are going to find its slope using the slope formula: 

where

is the slope.

are the coordinates of the first point. 

are the coordinates of the second point.

Our first point is (25,53), so  and ; our second point is (30,59), so  and . Lets replace those values in our slope formula:

Now that we have our slope, we are going to use the point-slope formula to complete our linear model. Point-slope formula: 

where

is the slope.

are the coordinates of the first point.

We already know what those values are, so lets replace them in our formula:

We can conclude that the equation of the line that best fit our data is .

3. The slope represent that each time that  increases by 5 units,  increases 6 units. In the context of our model it means that every time the arm span increase 5 inches, the person's height increases 6 inches.

Remember that in a linear function of the form ,  is the y-intercept. Knowing this, we can infer that the y-intercept of our model is 23. The y-intercept represent that when the arm span of a person is 0 inches, their height is 23, which doesn't make much sense. This is a perfect example why you shouldn't trust models every time. 

4. The residual () is the difference between the observable y-value -in our case the person's height, and the y-value in our linear equation. In other words: 

observable y-value - predicted y-value.

Lets fin our residuals using that formula:

(24,-0.8)

(24, 4.2)

(25, 1)

(26,-0.2)

(26,1.8)

(27,-1.4)

(29,-2.8)

(29,0.2)

Now, we are going to plot a residual plot using our residual points. If the residual plot (picture 1) does not follow a pattern, our linear model is a good fit for the data, but if the residual plot, follows a pattern our linear model is not a good fit for the data.

Since our residual plot does not follow any pattern, we can conclude that our linear model is a good fit for the data.

5. To find how tall is a person whose arm span is 66 inches, we just need to replace  with 66 in our linear equation and simplify: inches

We can conclude that a person whose arm span is 66 inches is 102.2 inches tall.

6. To find the arm span of a 74-inch-tall person, we are going to replace  with 64 in our linear equation an solve for : inches

We can conclude arm span of a 74-inch-tall person is 42.5 inches.

Step-by-step explanation:

where is the rest of the

step-by-step explanation: