To determine the equation of the line of best fit for the given dataset, we need to calculate the slope and the y-intercept of the line. Let's break down the process:
1. Listing the data points:
- [tex]\( (5, 4) \)[/tex]
- [tex]\( (6, 6) \)[/tex]
- [tex]\( (9, 9) \)[/tex]
- [tex]\( (10, 11) \)[/tex]
- [tex]\( (14, 12) \)[/tex]
2. Calculate the slope (m) and y-intercept (b):
The formula for the slope [tex]\( m \)[/tex] and y-intercept [tex]\( b \)[/tex] of the line of best fit using least squares regression are:
[tex]\[ m = \frac{N(\sum xy) - (\sum x)(\sum y)}{N(\sum x^2) - (\sum x)^2} \][/tex]
[tex]\[ b = \frac{(\sum y)(\sum x^2) - (\sum x)(\sum xy)}{N(\sum x^2) - (\sum x)^2} \][/tex]
Where [tex]\( N \)[/tex] is the number of data points.
Upon processing the given data:
- The calculated slope is approximately [tex]\( 0.894 \)[/tex]
- The calculated y-intercept is approximately [tex]\( 0.535 \)[/tex]
3. Form the equation:
Using the rounded values of the slope and y-intercept, the equation of the line of best fit is:
[tex]\[ y = 0.894x + 0.535 \][/tex]
4. Selecting the correct answer:
Among the multiple choices provided:
A. [tex]\( y = 0.894x + 0.535 \)[/tex]
B. [tex]\( y = 0.535x + 0.894 \)[/tex]
C. [tex]\( y = -0.535x + 0.894 \)[/tex]
D. [tex]\( y = -0.894x + 0.535 \)[/tex]
The correct equation of the line of best fit based on our calculations is:
A. [tex]\( y = 0.894x + 0.535 \)[/tex]
