Answer:
Linear approximation is given by: [tex]y = \frac{x}{5}+2[/tex]
Step-by-step explanation:
We are given the following information in the question:
Number of citations: 5 7.5 10 15 20
Outputs Residuals: 3 6 10 5 6
We have to find the linear approximation of the data that passes through the points (5, 3) and (20, 6).
Linear approximation is given by:
The equation of line is given by:
[tex](y-y_1) = \displaystyle\frac{y_2-y_2}{x_2-x_1}(x-x_1)[/tex]
where, [tex](x_1,y_1), (x_2.y_2)[/tex] is the point through which the line passes.
The equation of line is:
[tex](y-3) = \displaystyle\frac{6-3}{20-5}(x-5)\\\\15(y-3)= 3(x-5)\\15y = 3x-15+45\\15y = 3x + 30\\y = \frac{x}{5}+2[/tex]
The above equation is the required linear approximation.
