Question

using the line of best fit, what is the expected height given the shoe size is 7.5?
shoe size
height (in)
8.5
67
9.5
70
11
73.5
12
75
13
78
8
66
65.5 in
68.3 in
57.2 in
75.3 in

Explanation:

Step1: Calculate the slope ($m$)

The formula for slope is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Let's take two points, say $(x_1,y_1)=(8,66)$ and $(x_2,y_2)=(12,75)$.
$m=\frac{75 - 66}{12 - 8}=\frac{9}{4}=2.25$

Step2: Calculate the y - intercept ($b$)

Using the point - slope form $y=mx + b$ and the point $(8,66)$.
$66=2.25\times8 + b$
$66 = 18 + b$
$b=66 - 18=48$

Step3: Find the height for shoe size $x = 7.5$

Substitute $x = 7.5$ into the equation $y=2.25x + 48$
$y=2.25\times7.5+48$
$y = 16.875+48$
$y=64.875\approx65.5$

Answer:

65.5 in