Unformatted text preview: 5x − 3.446. It has R2 =
0.93765 which isn’t bad. The graph of y = p3 (x) in the viewing window [−1, 13] × [0, 24]
along with the scatter plot is shown below on the left. Notice that p3 hits the x-axis at about
x = 12.45 making this a bad model for future predictions. To use the model to approximate
the number of hours of sunlight on your birthday, you’ll have to ﬁgure out what decimal value 196 Polynomial Functions
of x is close enough to your birthday and then plug it into the model. My (Jeﬀ’s) birthday
is July 31 which is 10 days after July 21 (x = 7). Assuming 30 days in a month, I think
x = 7.33 should work for my birthday and p3 (7.33) ≈ 17.5. The website says there will be
about 18.25 hours of daylight that day. To have 14 hours of darkness we need 10 hours of
daylight. We see that p3 (1.96) ≈ 10 and p3 (10.05) ≈ 10 so it seems reasonable to say that
we’ll have at least 14 hours of darkness from December 21, 2008 (x = 0) to February 21, 2009
(x = 2) and then again from October 21,2009 (x = 10) to December 21, 2009 (x = 12).
The quartic regression model is p4 (x) = 0.0144x4 − 0.3507x3 + 2.259x2 − 1.571x + 5.513. It has
R2 = 0.98594 which is good. The graph of y = p4 (x) in the...
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