A linear model that best fits the overall pattern of points is given by the
regression line of the data.
- a. Please find attached the graph showing the linear model of the scatter plot created with MS Excel.
- b. The slope of the line is -6.2173.
- c. The relationship is as the price per Serving increases by 1 cent, the sodium per Serving decreases by -6.2173 mg.
Reasons:
a. Points on the graph are;
(6, 218),
The slope, b, regression line equation is given by the following formula;
[tex]b = \mathbf{\dfrac{\sum \left(x_i - \overline x\right) \times \left(y_i - \overline y\right) }{\sum \left(x_i - \overline x\right )^2 }}[/tex]
The regression line equation is; [tex]\overline y = b \cdot \overline x + a[/tex]
Where;
[tex]\overline x[/tex] = 18.732
[tex]\overline y[/tex] = 187.24
[tex]\sum \left(x_i - \overline x\right) \times \left(y_i - \overline y\right)[/tex] = -4926.59
[tex]\sum \left(x_i - \overline x\right )^2[/tex] = 792.3944
Therefore;
[tex]b = \dfrac{-4926.59}{792.3944 } \approx -6.2173[/tex]
[tex]a = \overline y - b \cdot \overline x[/tex]
Which gives;
a = 187.24 - (-6.2173) × 18.732 ≈ 303.70
The equation of the line is therefore; [tex]\overline y = \mathbf{-6.2173 \cdot \overline x + 303.70}[/tex]
Using the above regression line equation, the linear model of the scatter
plot can be drawn as presented in the graph created with MS Excel.
b. The slope of the line is b = -6.2173
c. The relationship between price per serving and sodium per serving is
as follows;
When the price per serving increases by 1 cent, the sodium per serving
decreases by 6.2173 mg.
Learn more about the regression line formula here:
https://brainly.com/question/14747095
