Project #7939 - Quadratic Model Project

Curve-fitting Project - Quadratic Regression Model




Quadratic Regression (QR)


For this project, you are supplied with the data to analyze.


Data: On a particular day in April, 2012, the outdoor temperature was recorded at 8 times of the day, and the following table was compiled.


Time of day (hour) Temperature (degrees F.)
7 35
9 50
11 56
13 59
14 61
17 62
20 59
23 44


REMARKS: The times are the hours since midnight. For instance, 7 means 7 am, and 13 means 1 pm.


The temperature is low in the morning, reaches a peak in the afternoon, and then decreases.


Tasks for Quadratic Regression Model (QR)


(QR-1) Plot the points (x, y) to obtain a scatterplot. Note that the trend is definitely non-linear. Use an appropriate scale on the horizontal and vertical axes and be sure to label carefully.


(QR-2) Find the quadratic polynomial of best fit and graph it on the scatterplot. State the formula for the quadratic polynomial.


(QR-3) Find and state the value of r2, the coefficient of determination. Discuss your findings. (r2 is calculated using a different formula than for linear regression. However, just as in the linear case, the closer r2 is to 1, the better the fit.) Is a parabola a good curve to fit to this data?


(QR-4) Use the quadratic polynomial to make an outdoor temperature estimate. Each class member will compute a temperature estimate for a different time of day. Look at the Class Members list in our Webtycho classroom, and look for the number "n" to the left of your name in the list. Take your number n, multiply it by 0.5 and add to 6 to get a time x in hours; that is, compute x = 0.5n + 6. The value of x is the time you will substitute into the quadratic polynomial to make a temperature estimate. For instance, for Basiru, n = 1 in the list, and for Basiru, x = 0.5(1) + 6 = 6.5 hours.


As another example, if n is 15, then x = 0.5(15) + 6 = 13.5 hours (1:30 pm), and then you would substitute x = 13.5 into your polynomial equation to get the corresponding outdoor temperature estimate for 1:30 pm. State your results clearly -- the time of day and the corresponding outdoor temperature estimate.

(QR-5) Using algebra (as in Chapter 3), find the maximum temperature predicted by the quadratic model and find the time when it occurred. Show work. Report the time to the nearest quarter hour (i.e., _:00 or __:15 or __: 30 or __:45) . (For instance, a time of 18.25 hours is 6:15 pm). Report the maximum temperature to the nearest tenth of a degree


Technology Tips

To complete the Quadratic Model portion of the project, you will need to use technology (or hand-drawing) to create a scatterplot, find a regression curve, plot the regression curve, and find r2.


For the given set of data, you will carry out quadratic regression .


Below are some options, together with a video. The video is limited to 5 minutes or less. It takes a bit of time for the video to initially download. When playing the video, if you want to slow it down to read the text, hit the pause icon. (If you run the mouse over the bottom of the video screen, the video controls will appear.)  You may need to adjust the volume.


The basic options are to:


    (1) Generate by hand and scan. 


    (2) Use Microsoft Excel.


    (3) Use Open Office.


    (4) Use a hand-held graphing calculator 


    (5) Use an online tool 


The free online graphing calculator at  (see picture)  allows you to find the quadratic curve and create a scatter plot. For more on this tool, see the Technology Tips for the Linear Model portion of the project.


The result of the free tool is not as nice looking as the Microsoft Excel version, but it is free.

See attached Word sample of Linear Model Project - please format in similar style.





Subject Mathematics
Due By (Pacific Time) 06/21/2013 08:00 pm
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