Question

shane created a scatter plot and drew a line of best fit, as shown. a scatter plot has data points (2, 9), (3, 12), (5, 11), (8, 13), (10, 12), (12, 11), (13, 14), (17, 12), and (18, 15). a diagonal fits two points. the maximum ranges of points lie above and below the curve. what is the equation of the line of best fit that shane drew?

Answer 1

The equation of the line of best fit that Shane drew can be found using the least-squares regression method.

Step-by-step explanation:

The equation of the line of best fit that Shane drew can be found by using the least-squares regression method. To find the equation, we need to calculate the slope and y-intercept of the line.

1. To find the slope, we use the formula:

• slope = (NΣXY - (ΣX)(ΣY)) / (NΣX^2 - (ΣX)^2)

To find the y-intercept, we use the formula:

• y-intercept = (ΣY - slope(ΣX)) / N

Using the given data points:

• (2, 9), (3, 12), (5, 11), (8, 13), (10, 12), (12, 11), (13, 14), (17, 12), and (18, 15)

we can calculate the slope and y-intercept to find the equation of the line of best fit.

Answer 2

The equation of the line of best fit is: y = 1/5x + 10. Option C

How do we find the equation of the line of best fit?

To find the equation of the line of best fit, we can identify identify points on the line.

Some points on the diagonal line are t (0,10) (5, 11) (10,12)

Lets find slope

m = (y₂ - y₁)/(x₂ - x₁)

m = (11-10)/(5-0)

m = 1/5

Or we could use points (5, 11) (10,12)

m = (y₂ - y₁)/(x₂ - x₁)

m = (12-11)/(10-5)

m = 1/5

Since the line passes through the y-axis at y=10 when x=0, the y-intercept (b) is 10.

y = 1/5x + 10