Question

Would like scatter plot image with line of best fit on the plot

1.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.


2.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.


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


4.Test the residuals of two other points to determine how well the line of best fit models the data.


5.Use the line of best fit to help you to describe the data correlation.


6.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?


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


Arm Span on Left, Height on Right

58 60

49 47

51 55

19 25

37 39

44 45

47 49

36 35

41 40

46 50

58 61

68 66

Answer 1

Here's what I get.

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

(DOWN BELOW)

This gave the regression equation:

y = 1.0595x - 4.1524

(c) Interpretation

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

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

(ii) Arm span of 74 in tall person

Answer 2

Just take it in co-ordinate pairs

• (x,y)=(Arm span,Height)

Take two points

• (58,60)
• (41,40)

Slope:-

`\\ \sf\longmapsto m=(40-60)/(41-58)`

`\\ \sf\longmapsto m=(-20)/(-17)`

`\\ \sf\longmapsto m=(20)/(17)`

`\\ \sf\longmapsto m\approx 1.2`

Equation of line in point slope form

`\\ \sf\longmapsto y-y_1=m(x-x_1)`

`\\ \sf\longmapsto y-60=1.2(x-58)`

`\\ \sf\longmapsto y-60=1.2x-69.6`

`\\ \sf\longmapsto 1.2x-y-9.6=0`

• Convert to slope intercept form y=mx+b

`\\ \sf\longmapsto y=1.2x-9.6`

Graph attached