Question

10) 4 4.5 5 5 5.5 6 Y | 0.5 0.6 0.8 LE 0.9 1.2 Which is most likely the equation of the line of best fit for the data given in the table? DELLE А y=034X=09 B y = 0.25x -0.7 с y =0.45x = 1 y=0.50 x -0.6

Answer 1

y = 0.34x - 0.9 (Option A)

We are given the data and we want to find the line of best fit.

The line of best fit is a line that goes through the data points and it gives the best representation of the spread of the data.

The equation of a line is given as:

y = mx + c

y represents y-values

x represents x-values

m is the slope of the line

c is the y-intercept of the line or where the line crosses the y-axis.

To get this equation for this question, we need to find both m and c.

In order to do this, the formulas are given below:

While for c or the y-intercept, we have:

`\begin{gathered} c=\bar{Y}-m\bar{X} \\ \text{where Y and X retain their same meaning from before} \end{gathered}`

Before we can calculate m and c, we need to calculate the means of both x and y values give to us.

This is done below:

Now we can proceed to get the slope m of our line.

In order to be tidy, we shall use a table to solve. This table is shown in the image below:

Thus, we can now calculate our slope m:

`\begin{gathered} M=\frac{\sum(x_i-\bar{\bar{X})(y_i-\bar{Y)}}}{\sum(x_i-\bar{X)^2}} \\ \\ M=((-1)(-0.3)+(-0.5)(-0.2)+0(0)+(0.5)(0.1)+(1)(0.4))/(1+0.25+0+0.25+1) \\ \\ M=(0.3+0.1+0+0.05+0.4)/(2.5)=0.34 \end{gathered}`

Therefore the slope (m) = 0.34

Now to calculate intercept (c)

`\begin{gathered} c=\bar{Y}-m\bar{X} \\ \bar{Y}=0.8\text{ (from previous calculation above)} \\ \bar{X}=5\text{ (from previous calculation above)} \\ \\ c=0.8-0.34*5 \\ c=0.8-1.7=-0.9 \end{gathered}`

Therefore, the intercept (c) = - 0.9

Bringing it all together, we can write the equation of the line as:

y = 0.34x - 0.9

Therefore the answer is: y = 0.34x - 0.9 (Option A)