The data in the table represents the average number of daylight ours each month in Springfield in 2015, rounded to the nearest quarter-hour.
Jan~9.5 hrs
Feb~10.5 hrs
Mar~12 hrs
Apr~13.25 hrs
May~14.5 hrs
Jun~15 hrs
Jul~14.75 hrs
Aug~13.75 hrs
Sep~12.5 hrs
Oct~11 hrs
Nov~9.75 hrs
Dec~9.25 hrs
Write an equation that best models the data.
What is the expected number of daylight hours in March 2020? Explain.
No it’s not
getting phase and average right
a - b cos(2pi(m-1)/11)
about
12.1 - 2.6 cos [ 2 pi(m-1)/11 ]
using average for a, min at m = 1
You are welcome :)
Does anyone know how to come up with this equation?
Damon can you help me in any way?
sine wave with period of one year
a + b sin 2 pi ( m-1)/11
m = 1 for January
m = 12 for December (you might need to adjust that to 1/2 month or something)
In march it says 12 hours.
TODAY March 20, the sun crosses the equator and it is 12 dark and 12 light all over this world !
Google spring equinox !!!!!!
Thank you Damon:)
What is the answer? is this answer correct?
To write an equation that best models the data, we can use a linear regression equation. A linear regression equation is of the form y = mx + b, where y represents the dependent variable (the average number of daylight hours), x represents the independent variable (the month), m represents the slope (the rate of change in daylight hours per month), and b represents the y-intercept (the average number of daylight hours in the starting month).
Based on the given data, we have the following values:
x = 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 (representing the months)
y = 9.5, 10.5, 12, 13.25, 14.5, 15, 14.75, 13.75, 12.5, 11, 9.75, 9.25 (representing the average number of daylight hours)
To find the slope (m), we can use the formula:
m = (sum(xy) - (sum(x) * sum(y)) / (sum(x^2) - (sum(x))^2
To find the y-intercept (b), we can use the formula:
b = (sum(y) - (m * sum(x))) / n
where n is the number of data points, in this case, 12.
Calculating the required values, we find:
sum(x) = 78
sum(y) = 138
sum(xy) = 1473.25
sum(x^2) = 650
(sum(x))^2 = 6084
Using these values in the formulas, we can find the slope and the y-intercept as:
m = (1473.25 - (78 * 138)) / (650 - 6084) = -0.485
b = (138 - (-0.485 * 78)) / 12 = 11.243
Therefore, the linear regression equation can be written as:
y = -0.485x + 11.243
Now, to find the expected number of daylight hours in March 2020, we need to substitute x = 27 into the equation, as March is the 27th month (assuming January 2015 is the starting month).
Using the equation, we have:
y = -0.485(27) + 11.243
y ≈ 9.068
Therefore, the expected number of daylight hours in March 2020 is approximately 9.068 hours.