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Sinusoidal Data Worksheet
West Coast Tidal Analysis: Fill in the following chart for the 2 low tide and 2 high tides per day for the researched two-day period (so four low tides and high tides all inter-distributed) for the Central or Southern California Coastal Region assigned to you… see : http://tbone.biol.sc.edu/tide/sites_uswest.html
Time elapsed since midnight of first day, t
Height of tide, h(t)
Low (L) or High (H) Date Time (PDT)
(decimal form : rounded to closest hundredth)
(feet) Tide
Load third and fourth columns into L (^) 1 & L (^) 2 , into your graphing calculator,
respectively. Make sure you are in RAD (radian) mode on your graphing calculator.
Turn ON your STAT PLOT to graph a scatter plot of L (^) 1 & L (^) 2 data in Plot1 with the
default “box” marker for the “points” from the ordered pairs.
Push ZOOM 9 to activate the ZoomStat feature to look at the “plotted” data points.
Alter the WINDOW settings as desired, to establish “buffers” as explained in class.
Perform a Sinusoidal Regression on L (^) 1 & L (^) 2 by using the following :
STAT > CALC (scroll down to option “C” [SinReg] and press enter) That will post the SinReg command to the home screen, and now you will need to follow that command with 5 items (# of iterations, X-list variable, Y-list variable, period guess, & Y 1 (to store the regression equation into Y 1 [the first equation in the Y= menu] for
future graphing purposes), each separated by commas. Insert “3” for the # of iterations, L (^) 1 for the X-list variable , L (^) 2 for the Y-list variable, and “12” for the period guess
(since there are two cycles of a low and high tide for each 24 hour day). Remember that you get the Y 1 “pasted in” from the list off Y= variables through the following : VARS >
` > ENTER > 1.
Your home screen should look like : SinReg 3, L (^) 1 , L (^) 2 , 12, Y 1
Press Enter to perform the regression…
Interpret the regression equation, by answering the following questions:
Round all four of the values of a , b, c , & d [of y = a ⋅ sin( bx + c )+ d ] to 2 decimal
places, and state the regression equation in the blank space below:
_____________________________________________
What is the relevance of the value for “a”?
What is the relevance of the value for “d”?
How are the “a” and “d” values inter-related?
From the “b” value, find the period of this model (sinusoidal regression).
Was it close to the guess you “seeded” the regression with?
Why is the period from the regression, the value that it is?
What is the significance of the “c” value? Find
c b
and explain it’s relevance to this data
set… Remember that y = a ⋅ sin( bx + c ) + d is equivalent to sin( ( ))
c b
y = a ⋅ b x + + d.
Average Daily U.S. Temperature Analysis: Fill in the following chart for the 12 average daily temperatures for the 15th^ day of every month (January-December) of 2007 for the United States City assigned to you… see : http://www.engr.udayton.edu/weather/citylistUS.htm
Data Point for time
Average Daily Temperature (°F), T Month Day Year (t) T(t) January 15 2007 1 February 15 2007 2 March 15 2007 3 April 15 2007 4 May 15 2007 5 June 15 2007 6 July 15 2007 7 August 15 2007 8 September 15 2007 9 October 15 2007 10 November 15 2007 11 December 15 2007 12
Load last two columns into L (^) 3 & L (^) 4 , into your graphing calculators, respectively.
Turn OFF your STAT PLOT for the L (^) 1 & L (^) 2 data from the tidal analysis in Plot
Turn ON your STAT PLOT to graph a scatter plot of L (^) 3 & L (^) 4 data in Plot2 with the
default “box” marker for the “points” from the ordered pairs.
Push ZOOM 9 to activate the ZoomStat feature to look at the “plotted” data points.
Alter the WINDOW settings as desired, to establish “buffers” as explained in class.
Perform a Sinusoidal Regression on L (^) 3 & L (^) 4 by using the following :
STAT > CALC (scroll down to option “C” [SinReg] and press enter) That will post the SinReg command to the home screen, and now you will need to follow that command with 5 items (# of iterations, X-list variable, Y-list variable, period guess, & Y 2 (to store the regression equation into Y 2 [the second equation in the Y= menu] for
future graphing purposes), each separated by commas. Insert “3” for the # of iterations, L (^) 3 for the X-list variable , L (^) 4 for the Y-list variable, and “12” for the period guess
(since the twelve months of a year determine the cyclical period by which our four seasons “cycle”, and thus determined the number of data points for this sinusoidal analysis). Remember that you get the Y 2 “pasted in” from the list off Y= variables
through the following : VARS > ` > ENTER > 2.
Your home screen should look like : SinReg 3, L (^) 3 , L (^) 4 , 12, Y 2
Press Enter to perform the regression…
Interpret the regression equation, by answering the following questions:
Round all four of the values of a , b, c , & d [of y = a ⋅ sin( bx + c )+ d ] to 2 decimal
places, and state the regression equation in the blank space below:
_____________________________________________
What is the relevance of the value for “a”?
What is the relevance of the value for “d”?
How are the “a” and “d” values inter-related?
From the “b” value, find the period of this model (sinusoidal regression).
Was it close to the guess you “seeded” the regression with?
Why is the period from the regression, the value that it is?
What is the significance of the “c” value? Find c b
and explain it’s relevance to this data
set… Remember that y = a ⋅ sin( bx + c ) + d is equivalent to sin( ( )) c b
y = a ⋅ b x + + d.
Average Daily World Temperature Analysis: Fill in the following chart for the 24 Hour Average Temperature data you retrieve for the 12 months (January-December) of several of the last years for the World City that you pick. This world city cannot be picked yet (see the edublog @ : http://reverest.edublogs.org to see if the city you want has been taken yet … remember to post your initials and world city on the blog, so you all get different cities) … see : http://www.worldclimate.com for getting your data, once you have deduced “your city” is available for analysis…
Data Point for time
Average Daily Temperature (°F), T
Month (t) T(t) January 1 February 2 March 3 April 4 May 5 June 6 July 7 August 8 September 9 October 10 November 11 December 12
Load last two columns into L 5 (^) & L 6 , into your graphing calculators, respectively.
Turn OFF your STAT PLOTS for the L (^) 1 & L (^) 2 AND L (^) 3 & L (^) 4 data from the tidal &
U.S. city analyses in Plot1 & Plot Turn ON your STAT PLOT to graph a scatter plot of L 5 (^) & L 6 data in Plot3 with the
default “box” marker for the “points” from the ordered pairs.
Push ZOOM 9 to activate the ZoomStat feature to look at the “plotted” data points.
Alter the WINDOW settings as desired, to establish “buffers” as explained in class.
Perform a Sinusoidal Regression on L 5 (^) & L 6 by using the following :
STAT > CALC (scroll down to option “C” [SinReg] and press enter) That will post the SinReg command to the home screen, and now you will need to follow that command with 5 items (# of iterations, X-list variable, Y-list variable, period guess, & Y 3 (to store the regression equation into Y 3 [the third equation in the Y= menu] for
future graphing purposes), each separated by commas. Insert “3” for the # of iterations, L 5 for the X-list variable , L 6 for the Y-list variable, and “12” for the period guess (since
the twelve months of a year determine the cyclical period by which our four seasons “cycle”, and thus determined the number of data points for this sinusoidal analysis). Remember that you get the Y 3 “pasted in” from the list off Y= variables through the
following : VARS > ` > ENTER > 3.
Your home screen should look like : SinReg 3, L 5 , L 6 , 12, Y 3
Press Enter to perform the regression… Interpret the regression equation, by answering the following questions:
Round all four of the values of a , b, c , & d [of y = a ⋅ sin( bx + c )+ d ] to 2 decimal
places, and state the regression equation in the blank space below:
_____________________________________________
What is the relevance of the value for “a”?
What is the relevance of the value for “d”?
How are the “a” and “d” values inter-related?
From the “b” value, find the period of this model (sinusoidal regression).
Was it close to the guess you “seeded” the regression with?
Why is the period from the regression, the value that it is?
What is the significance of the “c” value? Find c b
and explain it’s relevance to this data
set… Remember that y = a ⋅ sin( bx + c ) + d is equivalent to sin( ( )) c b
y = a ⋅ b x + + d.
Graph the regression equation you found with your graphing calculator on the provided graph paper below:
