The equation of the line of best fit is y = -4.75X + 88.6 and the absolute value of the correlation coefficient is 0.906
<h3>The equation of the line of best fit</h3>
The data values of the question are as follows:
(1, 88), (2, 75), (3, 71), (4, 69), (5,66), (6, 68), (7, 50)
To determine the equation of the line of best fit, we make use of a graphing calculator.
From the graphing calculator, we have the following summary:
- Sum of X = 28
- Sum of Y = 487
- Mean X = 4
- Mean Y = 69.5714
- Sum of squares (SSX) = 28
- Sum of products (SP) = -133
- The value of R is: -0.906.
The line of best fit equation is
y = bx + a
Where
b = SP/SSX = -133/28 = -4.75
a = MY - bMX = 69.57 - (-4.75*4) = 88.57143
So, we have:
y = -4.75X + 88.57143
Approximate
y = -4.75X + 88.6
Hence, the equation of the line of best fit is y = -4.75X + 88.6
<h3>The absolute value of the
correlation coefficient</h3>
In (a), we have:
The value of R is: -0.906.
This represents the correlation coefficient.
The absolute value is
|R| = 0.906.
Hence, the absolute value of the correlation coefficient is 0.906
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