Write the equation of a trend line.

{(-10, 3), (-5, 1), (-1, -4), (3, -7), (12, -12)}
How do I do this problem?

To find the equation of a trend line, you can use the method of linear regression. Here are the steps to follow:

Step 1: Make a table of the given data points:

x | y
-------------
-10 | 3
-5 | 1
-1 | -4
3 | -7
12 | -12

Step 2: Calculate the sum of x, y, x^2, and xy. Also, find the number of data points (n) and the average of x and y.

For the given data set:
Σx = -10 + (-5) + (-1) + 3 + 12 = -1
Σy = 3 + 1 - 4 - 7 - 12 = -19
Σx^2 = (-10)^2 + (-5)^2 + (-1)^2 + 3^2 + 12^2 = 239
Σxy = (-10)(3) + (-5)(1) + (-1)(-4) + (3)(-7) + (12)(-12) = 201
n = 5
¯x = Σx / n = -1 / 5 = -0.2
¯y = Σy / n = -19 / 5 = -3.8

Step 3: Calculate the slope (m) of the trend line using the formula:
m = (Σxy - n * ¯x * ¯y) / (Σx^2 - n * ¯x^2)

Substituting the values:
m = (201 - 5 * (-0.2) * (-3.8)) / (239 - 5 * (-0.2)^2)

Simplifying:
m = 0.062

Step 4: Calculate the y-intercept (b) of the trend line using the formula:
b = ¯y - m * ¯x

Substituting the values:
b = -3.8 - 0.062 * (-0.2)

Simplifying:
b = -3.794

Step 5: Write the equation of the trend line in slope-intercept form (y = mx + b):

y = 0.062x - 3.794

So, the equation of the trend line is y = 0.062x - 3.794.

To find the equation of a trend line, you will need to use the method of least squares. Here's how you can do it step by step:

Step 1: Calculate the mean (average) of both the x-values and y-values in the given dataset.

For the x-values: (-10 + -5 + -1 + 3 + 12) / 5 = -1.8
For the y-values: (3 + 1 - 4 - 7 - 12) / 5 = -3

Step 2: Calculate the differences between each x-value and the mean of x, and the corresponding differences between each y-value and the mean of y.

For the x-values:
-10 - (-1.8) = -8.2
-5 - (-1.8) = -3.2
-1 - (-1.8) = 0.8
3 - (-1.8) = 4.8
12 - (-1.8) = 13.8

For the y-values:
3 - (-3) = 6
1 - (-3) = 4
-4 - (-3) = -1
-7 - (-3) = -4
-12 - (-3) = -9

Step 3: Multiply the differences obtained above for both x and y. Calculate the sum of these products.

Multiply the x-differences and y-differences:
(-8.2 * 6) + (-3.2 * 4) + (0.8 * -1) + (4.8 * -4) + (13.8 * -9) = -227.2

Step 4: Calculate the sum of the squared differences in x-values.

(-8.2)^2 + (-3.2)^2 + (0.8)^2 + (4.8)^2 + (13.8)^2 = 415.8

Step 5: Calculate the equation of the trend line.

The equation of the trend line is given by the formula:
y = mx + b

Where m represents the gradient (slope) and b represents the y-intercept.

The gradient m is calculated using the formula:
m = (Sum of (x - mean of x) * (y - mean of y)) / (Sum of (x - mean of x)^2)

Using the values calculated earlier in steps 1, 2, and 3:
m = (-227.2) / (415.8) ≈ -0.547

To find the y-intercept b, substitute the values of x and y means, and the gradient into the formula:
-3 = (-0.547) * (-1.8) + b

Simplifying:
-3 = 0.9836 + b
b ≈ -3.9836

Therefore, the equation of the trend line is:
y = -0.547x - 3.9836

google equation of trend line for lots of help and examples.