Write an equation for the trend line and predict the value when x is 15.

x y
0 17.5
3 35.4
6 50.5
9 60.6
12 66.3

there are lots of linear regression calculators online, such as

http://ncalculators.com/statistics/linear-regression-calculator.htm

To find the equation for the trend line, we can use the method of least squares. This method finds the line that minimizes the sum of the squared differences between the actual y-values and the predicted y-values on the line.

Step 1: Calculate the means
Find the mean (average) of the x-values and the mean of the y-values:
mean_x = (0 + 3 + 6 + 9 + 12) / 5 = 6
mean_y = (17.5 + 35.4 + 50.5 + 60.6 + 66.3) / 5 = 46.86

Step 2: Calculate the deviations
Find the deviations of each x-value from the mean x-value and the deviations of each y-value from the mean y-value:
deviation_x = [0 - 6, 3 - 6, 6 - 6, 9 - 6, 12 - 6] = [-6, -3, 0, 3, 6]
deviation_y = [17.5 - 46.86, 35.4 - 46.86, 50.5 - 46.86, 60.6 - 46.86, 66.3 - 46.86] = [-29.36, -11.46, 3.64, 13.74, 19.44]

Step 3: Calculate the squared deviations
Square each deviation:
squared_deviation_x = [(-6)^2, (-3)^2, 0^2, 3^2, 6^2] = [36, 9, 0, 9, 36]
squared_deviation_y = [(-29.36)^2, (-11.46)^2, (3.64)^2, (13.74)^2, (19.44)^2] = [860.3296, 131.3316, 13.2496, 188.9476, 378.5616]

Step 4: Calculate the product of deviations
Multiply the deviations of x with the deviations of y:
product_deviations = [-6 * -29.36, -3 * -11.46, 0 * 3.64, 3 * 13.74, 6 * 19.44] = [176.16, 34.38, 0.00, 41.22, 116.64]

Step 5: Calculate the slope and intercept
To calculate the slope (m) of the trend line, use the following formula:
m = ∑(product_deviations) / ∑(squared_deviation_x)
To calculate the intercept (b) of the trend line, use the following formula:
b = mean_y - (m * mean_x)

slope = (∑(product_deviations)) / (∑(squared_deviation_x)) = (176.16 + 34.38 + 0.00 + 41.22 + 116.64) / (36 + 9 + 0 + 9 + 36) = 368.40 / 90 = 4.0933
intercept = mean_y - (slope * mean_x) = 46.86 - (4.0933 * 6) = 46.86 - 24.56 = 22.30

So the equation for the trend line is:
y = 4.0933x + 22.30

To predict the value of y when x is 15, substitute x = 15 into the equation and solve for y:
y = 4.0933 * 15 + 22.30 = 61.40

Therefore, when x is 15, the predicted value for y is 61.40.