Sinusoidal Data Worksheet

Transcription

1 Sinusoidal Data Worksheet West Coast Tidal Analysis: Fill in the following chart for the low tide and 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 : Date Time (PDT) Time elapsed since midnight of first day, t (decimal form : rounded to closest hundredth) Height of tide, h(t) (feet) Low (L) or High (H) Tide Load third and fourth columns into L, 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 data in Plot 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 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 items (# of iterations, X-list variable, Y-list variable, period guess, & Y (to store the regression equation into Y [the first equation in the Y= menu] for future graphing purposes), each separated by commas. Insert for the # of iterations, L for the Y-list variable, and for the period guess L for the X-list variable, (since there are two cycles of a low and high tide for each hour day). Remember that you get the Y pasted in from the list off Y= variables through the following : VARS > > ENTER >. Your home screen should look like : SinReg, L, L,, 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 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 c set Remember that y = a sin( bx+ c) + d is equivalent to y = a sin( b( x+ )) + d. b

3 Graph the regression equation you found with your graphing calculator on the provided graph paper below: Could you alter the SINE regression equation to be a COSINE equation, from what you know about the relationship between the sine and cosine functions (I am referring to their out of phase relationship here )? What would that equation be? Why do you think that the regression equation didn t perfectly fit the data?

4 Average Daily U.S. Temperature Analysis: Fill in the following chart for the average daily temperatures for the th day of every month (January-December) of 007 for the United States City assigned to you see : Data Point for time Average Daily Temperature ( F), T Month Day Year (t) T(t) January 007 February 007 March 007 April 007 May 007 June July August September October November 007 December 007 Load last two columns into L, into your graphing calculators, respectively. Turn OFF your STAT PLOT for the L data from the tidal analysis in Plot Turn ON your STAT PLOT to graph a scatter plot of L data in Plot 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 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 items (# of iterations, X-list variable, Y-list variable, period guess, & Y (to store the regression equation into Y [the second equation in the Y= menu] for future graphing purposes), each separated by commas. Insert for the # of iterations, L for the X-list variable, L for the Y-list variable, and 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 pasted in from the list off Y= variables through the following : VARS > > ENTER >.

5 Your home screen should look like : SinReg, L, L,, Y 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 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 y = a sin( b( x+ )) + d. c b

6 Graph the regression equation you found with your graphing calculator on the provided graph paper below: Could you alter the SINE regression equation to be a COSINE equation, from what you know about the relationship between the sine and cosine functions (I am referring to their out of phase relationship here )? What would that equation be? Why do you think that the regression equation didn t perfectly fit the data?

7 Average Daily World Temperature Analysis: Fill in the following chart for the Hour Average Temperature data you retrieve for the 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 : 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 : for getting your data, once you have deduced your city is available for analysis Data Point for Average Daily Temperature ( F), T time Month (t) T(t) January February March April May June 6 July 7 August 8 September 9 October 0 November December Load last two columns into L 6, into your graphing calculators, respectively. Turn OFF your STAT PLOTS for the L AND L data from the tidal & U.S. city analyses in Plot & Plot Turn ON your STAT PLOT to graph a scatter plot of L 6 data in Plot 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 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 items (# of iterations, X-list variable, Y-list variable, period guess, & Y (to store the regression equation into Y [the third equation in the Y= menu] for future graphing purposes), each separated by commas. Insert for the # of iterations, L for the X-list variable, L 6 for the Y-list variable, and for the period guess (since

8 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 pasted in from the list off Y= variables through the following : VARS > > ENTER >. Your home screen should look like : SinReg, L, L 6,, Y 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 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 y = a sin( b( x+ )) + d. Graph the regression equation you found with your graphing calculator on the provided graph paper below: c b

9 Could you alter the SINE regression equation to be a COSINE equation, from what you know about the relationship between the sine and cosine functions (I am referring to their out of phase relationship here )? What would that equation be? Why do you think that the regression equation didn t perfectly fit the data? Did you expect the fit from the World Temperature Data to be a better or worse fit than the U.S City Data? [Hint: Consider the time period over which the data was collected for each analysis before reflecting & commenting.]