Answer:
The required equation is:
[tex]y=\mathbf{-0.271}x+\mathbf{13.876}[/tex]
Step-by-step explanation:
We have x = Distance of goal posts
y = field Goals made
The data given is:
x y
20 9
25 6
30 7
35 4
40 1
45 2
50 1
We need to find the regression equation y = bx + a
Where [tex]b=\frac{SP}{SS_x} \:and\: a=M_y-bM_x[/tex]
Sum of all values of x = 245
Sum of all values of y = 30
Now, calculating mean using formula: [tex]Mean=\frac{Sum\:of\:all|\:values}{Number\:of\:values}[/tex]
Mean of x (Mₓ) = 35
Mean of y ([tex]M_y[/tex]) = 4.28
Sum of squares (SSₓ) = 700
Sum of products (SP) = -190
Now, finding b:
[tex]b=\frac{SP}{SS_x} \\b=\frac{-190}{700}\\b=-0.271[/tex]
Now, finding a:
[tex]a=M_y-bM_x\\a=4.28-(-0.271*35)\\a=13.786[/tex]
So, the required equation is:
[tex]y=\mathbf{-0.271}x+\mathbf{13.876}[/tex]
