The equation of the line of best fit is [tex]y = -\frac{5}{6}x + \frac{82}{3}[/tex] and
We start by drawing an approximated line of best fit (see attachment)
From the attached graph, we have the following points:
(x, y) = (4, 24) and (28, 4)
The equation of the line of best fit is then calculated as:
[tex]y = \frac{y_2 -y_1}{x_2 -x_1} * (x - x_1) + y_1[/tex]
This gives
[tex]y = \frac{4 -24}{28 -4} * (x - 4) + 24[/tex]
Evaluate the difference
[tex]y = -\frac{20}{24} * (x - 4) + 24[/tex]
Simplify
[tex]y = -\frac{5}{6} * (x - 4) + 24[/tex]
Expand
[tex]y = -\frac{5}{6}x + \frac{10}{3} + 24[/tex]
Evaluate the sum
[tex]y = -\frac{5}{6}x + \frac{10 + 24*3}{3}[/tex]
[tex]y = -\frac{5}{6}x + \frac{82}{3}[/tex]
Hence, the equation of the line of best fit is [tex]y = -\frac{5}{6}x + \frac{82}{3}[/tex]
The time spent on TV is given as:
x = 15
So, we have:
[tex]y = -\frac 56 * 15 + \frac{82}3[/tex]
Evaluate the product
[tex]y = -\frac{75}6 + \frac{82}3[/tex]
Evaluate the sum
[tex]y = \frac{-75+164}6[/tex]
This gives
[tex]y = \frac{89}6[/tex]
Simplify
y = 15
Hence, the amount of time spent during homework is 15 hours for a student that spent 15 hours on TV
Read more about regression equations at:
https://brainly.com/question/17844286
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