The equation of the line of best fit for the data shown in the picture is y=0.894x+0.535
What is a straight line?
A straight line is a combination of endless points joined on both sides of the point.
We have a data in the table:
Let's suppose the equation for the line is:
y = mx + c
Where m is the slope of the line and c is the y-intercept.
The value of m is given by:
[tex]\rm m = \frac{S_{xy}}{S_{xx}} }[/tex] and
[tex]\rm S_{xy} = \sum_{i=1}^{n}x_iy_i-\frac{(\sum_{i=1}^{n}x_i)(\sum_{i=1}^{n}y_i)}{n}[/tex]
[tex]\rm S_{xx} = \sum_{i=1}^{n}x_i^2-\frac{(\sum_{i=1}^{n}x_i)^2}{n}[/tex]
From the table(data is not mentioned we have assumed the data) the values of [tex]\rm \sum_{i=1}^{n}x_iy_i= 415[/tex], [tex]\rm {\sum_{i=1}^{n}x_i= 44[/tex], [tex]\rm {\sum_{i=1}^{n}y_i= 42[/tex],
[tex]\rm {\sum_{i=1}^{n}x_i^2= 438[/tex], and n = 5.
[tex]\rm S_{xy}= 415-\frac{44\times42}{5} \Rightarrow 45.4\\\\\rm S_{xx}= 438- \frac{44^2}{5} \Rightarrow 50.8[/tex]
[tex]\rm m = \frac{45.4}{50.8} } \Rightarrow 0.8937 \approx0.894[/tex]
For c we have to calculate the means of x and y for this:
[tex]\rm \bar{x} = \frac{\sum x}{n} \Rightarrow \frac{44}{5} \Rightarrow8.8[/tex]
[tex]\rm \bar{y} = \frac{\sum y}{n} \Rightarrow \frac{42}{5} \Rightarrow8.4[/tex]
Now, put the above values in the equation of a line to find the value of c
8.4 = (0.894)(8.8)+c
c = 0.5328 ≈ 0.535
Now the line is y = 0.894x+0.535
Thus, the line of best fit for the data shown in the picture is y=0.894x+0.535
Learn more about the straight line here:
brainly.com/question/3493733
