Respuesta :
Answer: (a) y = 2.7394x - 118.1368
(b) R² = 0.8215 or 82.15%
Step-by-step explanation: Regression line is the best line that relates the variables in the data.
To calculate the fitted regression equation:
1) Calculate average of x-values ([tex]x_{i}[/tex]) and average of y-values ([tex]y_{i}[/tex]);
2) Calculate the slope, b, by doing:
[tex]b=\frac{\Sigma (x-x_{i})(y-y_{i})}{\Sigma (x-x_{i})^{2}}[/tex]
3) Calculate y-intercept, a, by doing:
[tex]a=y_{i}-bx_{i}[/tex]
4) Then, it gives regression equation: y = bx + a
For the data on chemical reactions:
(a) [tex]b=\frac{ [(136.24-105.3955)+...+(86.18-105.3955)].[(234.5-170.58)+...+(106-170.58)]}{(136.24-105.3955)^{2}+...+(86.18-105.3955)^{2}}[/tex]
b = 2.7394
[tex]a=170.58-2.7394(105.3955)[/tex]
a = -118.1368
y = 2.7394x - 118.1368
The fittest regression equation is y = 2.7394x - 118.1368.
(b) R is correlation coefficient and measures the strength of the relationship between the variables. It is calculated as:
[tex]R=\frac{n\Sigma(xy)-(\Sigma x)(\Sigma y)}{\sqrt{[n\Sigma x^{2}-(\Sigma x^{2})][n\Sigma y^{2}-(\Sigmay^{2})]} }[/tex]
For this fit, R = 0.9064
The variable R² is the coefficient of determination, is the square of correlation coefficient and is usually stated as a percent.
What the variable represents is the percent of variation in the dependent variable (y) explained by the variation in the independent variable (x).
For this fit:
[tex]R^{2} = 0.9064^{2}[/tex]
[tex]R^{2} =[/tex] 0.8215
What it entails is that 82.15% of the variation of retention time is due to the molecular weight of each chemical compound.
