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puteri [66]
3 years ago
7

Raquel throws darts at a coordinate grid centered at the origin. Her goal is to create a line of darts. Her darts actually hit t

he 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?

Mathematics
1 answer:
lora16 [44]3 years ago
7 0

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!!!

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