Question

scatter plot practice
due: january 20 at 3:00 pm
grade: 86%
answer
height (centimeters)
135 140 145 150 155 160 165 170 175 180
femur length (centimeters)
35 37 39 41 43 45 47 49 51 53 55
an expected height of 168.4 centimeters when the femur has a length of 50 centimeters.
an expected height of 50 centimeters when the femur has a length of 168.4 centimeters.
the height of an actual person
the height of an actual person

Explanation:

Step1: Identify line of best fit points

We use two clear points on the line: $(37, 140)$ and $(55, 180)$.

Step2: Calculate slope of the line

Slope $m = \frac{y_2 - y_1}{x_2 - x_1}$
$m = \frac{180 - 140}{55 - 37} = \frac{40}{18} = \frac{20}{9} \approx 2.222$

Step3: Find y-intercept (b)

Use $y = mx + b$ with $(37, 140)$:
$140 = \frac{20}{9}(37) + b$
$140 = \frac{740}{9} + b$
$b = 140 - \frac{740}{9} = \frac{1260 - 740}{9} = \frac{520}{9} \approx 57.778$

Step4: Write line equation

$y = \frac{20}{9}x + \frac{520}{9}$

Step5: Predict height for x=50

Substitute $x=50$:
$y = \frac{20}{9}(50) + \frac{520}{9} = \frac{1000 + 520}{9} = \frac{1520}{9} \approx 168.4$

Answer:

An expected height of 168.4 centimeters when the femur has a length of 50 centimeters.