We will see that the linear equation is:
y = 1.1*x -13.5
b) The predicted height is 164.7cm
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How to get the linear equation?</h3>
A general linear equation is:
y = a*x + b
Where a is the slope and b is the y-intercept.
If we know that the line passes through (x₁, y₁) and (x₂, y₂), then we can write the slope as:
a = (y₂ - y₁)/(x₂ - x₁)
In this case, the line passes through (165, 168) and (174, 178), then the slope is:
a = (178 - 168)/(174 - 165) = 10/9 = 1.1
Then the line is:
y = 1.1*x + b
To get the value of b, we use one of the given points, for example if we use the first one (165, 168) we must have x = 165 and y = 168, replacing that we get:
168 = 1.1*165 + b
168 - 1.1*165 = b = -13.5
The equation is:
y = 1.1*x -13.5
Now we want to find the height of a person with an arm span of 162cm, then we replace x by 162 to get:
y = 1.1*162 -13.5 = 164.7
The predicted height is 164.7cm
If you want to learn more about linear equations, you can read:
brainly.com/question/1884491
percent of data lies within 2 standard deviations of mean.