The equation of curve of best fit is y = -30.17x + 14.49. To find the curve of best fit, we would require two equations which are explained in details below.
Equation of Straight Line
Data;
- ∑x = 16
- ∑y = 50.9
- ∑x^2 = 35
- ∑xy = 24.6
The equation of straight line is y = ax + b
If we modify it to fit into this problem,
[tex]\sum y = na + b \sum X ... equ(i)\\\sum xy = a \sum x + b \sum x^2 ...equ(ii)[/tex]
Let's substitute the values into the equations and solve
[tex]\sum y = na + b \sum X ... equ(i)\\\sum xy = a \sum x + b \sum x^2 ...equ(ii)\\50.9 = 6*a + b*16 ...equ(i)\\24.6 = a*16 + b*35 ...equ(ii)\\50.9 = 6a + 16b ...equ(i)\\24.6 = 16a + 35b ...equ(ii)[/tex]
Let's solve both equation (i) and equation (ii)
[tex]50.9 = 6a + 16b...equ(i)\\24.6 = 16a + 35b ...equ(ii)\\a = -30.17, b = 14.49[/tex]
We can substitute the values of a and b into the equation
[tex]y = ax + b\\y = -30.17x + 14.49[/tex]
The equation of curve of best fit is y = -30.17x + 14.49
Learn more on equation of best fit on linear regression here;
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