Posted by grant on Saturday, May 12, 2007 at 9:20am.
The table shows the depth (d metres) of water in a harbour at certain times (t hours) after midnight on a particular day.
time t (hours)
and the in the next column corresponding to the figures above is
depth d (m)
Use the regression facilities on your calculator to fit a sine curve to these data. Choose the one option which provides the best fit model (with coefficient rounded to 2 significant figures).
Can anyone help me please. I may be d?
Note that you want d(t) to be of the form:
d(t) = A + B sin(r t + s)
Now, as you can see, all the options that express d like this have r = 0.49. This makes it easy to find the best fit, because you can now transform this problem into a linear regression problem as follows. You write:
d(t) = A + B sin(r t + s) =
A + B [cos(s) sin(r t) cos(s) + sin(s)cos(rt)(rt)] =
A + B cos(s) sin(rt) + B sin(s) cos(rt)
So, this problem is of the form:
d(t) = A_1 + A_2 f_2(t) +
f_2(t) = sin(rt)
f_3(t) = cos(rt)
So this is a standard linear regression problem as d is a linear function of f_2 and f_3.
You just need to proceed in the same way as you would proceed in case of a regression problem like:
Y = A + B X1 + C X2
for given data for Y, X1, and X2.
i'm not sure what you mean. which are the correct answers?
Count, please email me at firstname.lastname@example.org
Do you have a calculator in which you can enter data to do linear regression in multiple variables?
If so, then you need to do the following. Compile a table with the values of X1 = sin(0.49 t) and
X2 = cos(0.49 t).
Then you must enter the data for Y = d, X1 and X2 in your calculator and out will come the regression parameters corresponding to a fit of the form:
Y = A + B X1 + C X2
From B and C you then calculate the amplitude and the phase of the sin...
I've just emailed you :)
I don't have this type of calculator as yet and my homework is due on monday. Is the answer A?
Answer this Question
math - The table shows the depth (d metres) of water in a harbour at certain ...
9th grade math - The depth of water(d metres) in a harbour is given by the ...
math - The depth of water(d metres) in a harbour is given by the formula d = a+...
Math-calculus - At a certain point on the beach, a post sticks out of the sand, ...
Calculus - At a certain point on the beach, a post sticks out of the sand, its ...
Math - The tides at cape Capstan, New Brunswick, change the depth of the water ...
math help - Posted by grant on Saturday, May 12, 2007 at 9:20am. The table shows...
Maths - The average depth of the water in a port on a tidal river is 4 m. At low...
Trigonometric Functions - The average depth of the water in a port on a tidal ...
Trig functions - The average depth of the water in a port on a tidal river is 4m...