If this is a linear function between x and y, the slope will be constant.
We can pick any two ordered pairs, like (75, 2.3) and (82, 3) and calculate the slope as:
[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{3-2.3}{82-75}=\frac{0.7}{7}=0.1[/tex]
We can write the point-slope form of the equation and rearrange to find the value of the y-intercept and the slope-intercept form of the equation:
[tex]\begin{gathered} y-y_0=m(x-x_0) \\ y-3=0.1(x-82) \\ y=0.1x-0.1\cdot82+3 \\ y=0.1x-8.2+3 \\ y=0.1x-5.2 \end{gathered}[/tex]
We can test if the equation is correct with another point, like (65,2):
[tex]\begin{gathered} y=0.1x-5.2 \\ y(65)=0.1(65)-5.2 \\ y(65)=6.5-5.2 \\ y(65)=1.3 \end{gathered}[/tex]
This is not a exact line, so we have to apply a regression model to find the approximate line that best represent this relationship:
Answer: the linear regression model that best represents the relation between x and y is y=0.0736x-3.0166.
