Question

Raquel throws darts at a coordinate grid centered at the origin. Her goal is to create a line of darts. Her darts actually hit the coordinate grid at (–5, 0), (1, –3), (4, 5), (–8, –6), (0, 2), and (9, 6). Which equation best approximates the line of best fit of the darts?

Answer 1

Answer:

The line of best fit

y = 0.633x + 0.561

Step-by-step explanation:

The coordinates that the dart hit include

(–5, 0), (1, –3), (4, 5), (–8, –6), (0, 2), and (9, 6)

The x and y coordinates can be written as

x | y

-5|0

1 | -3

4|5

-8|-6

0|2

9|6

So, running the analysis on a spreadsheet application, like excel, the table of parameters is obtained and presented in the first attached image to this solution.

Σxᵢ = sum of all the x variables.

Σyᵢ = sum of all the y variables.

Σxᵢyᵢ = sum of the product of each x variable and its corresponding y variable.

Σxᵢ² = sum of the square of each x variable

Σyᵢ² = sum of the square of each y variable

n = number of variables = 6

The scatter plot and the line of best fit is presented in the second attached image to this solution

Then the regression analysis is then done

Slope; m = [n×Σxᵢyᵢ - (Σxᵢ)×(Σyᵢ)] / [nΣxᵢ² - (∑xi)²]

Intercept b: = [Σyᵢ - m×(Σxᵢ)] / n

Mean of x = (Σxᵢ)/n

Mean of y = (Σyᵢ) / n

Sample correlation coefficient r:

r = [n*Σxᵢyᵢ - (Σxᵢ)(Σyᵢ)] ÷ {√([n*Σxᵢ² - (Σxᵢ)²][n*Σyᵢ² - (Σyᵢ)²])}

And -1 ≤ r ≤ +1

All of these formulas are properly presented in the third attached image to this answer

The table of results; mean of x, mean of y, intercept, slope, regression equation and sample coefficient is presented in the fourth attached image to this answer.

Hope this Helps!!!