Question

A scatter plot and a possible line of best fit is shown:

A scatter plot is shown. Data points are located at 2 and 3, 4 and 2, 5 and 5, 6 and 7, 7 and 4, and 8 and 6. A line is drawn passing through 1 and 1 connecting to 8 and 7.

Is the line of best fit accurate for the data shown?

Yes, because it passes through the center of the data points
Yes, because it touches the y-axis
No, because the line does not touch any points
No, because the line should touch every point

Answer 1

The answer is: Yes, because it passes through the center of the data points

Answer 2

Option A) Yes, because it passes through the center of the data points

Explanation:

We are given the following information in the question:

A scatter plot is shown. Data points are located at 2 and 3, 4 and 2, 5 and 5, 6 and 7, 7 and 4, and 8 and 6. A line is drawn passing through 1 and 1 connecting to 8 and 7.

The equation of line is given by:

`(y-y_1) = \displaystyle(y_2-y_1)/(x_2-x_1)(x-x_1)`

Where
`(x_1,y_1), (x_2,y_2)` are the points through which the line passes.

Putting the values, we get the equation of line:

`y = \displaystyle(6x)/(7) + (1)/(7)`

The attached image shows the given scatter plot.

The line of best fit accurate for the data shown because as shown in the figure it passes through the center of the data points minimizing the perpendicular distance of each point from the line.