Clothing Sales

>>Clothing sales
tend to vary by season with more clothes sold
in spring and fall. The table below gives sales
figures for each month at a certain clothing store. We’re going to find the quartic
or fourth degree polynomial that best fits the data,
letting y equal the sales amount and x equal the month,
using x=1 for January. We’ll round all of
the coefficients to 3 decimal positions. And so let’s pull up the
graphing calculator and STAT 1 for EDIT. I’m going to go up
and CLEAR List 2, press ENTER. Go to the left, up,
CLEAR List 1 and ENTER. And now I’m ready to enter
the numbers from 1 to 12. These are the numbers
of the month in List 1. Each time I press the down arrow
before entering the next number. 6, 7, 8, 9, 10, 11
and finally 12. Now I move to the right, which
takes me to the top of List 2 where I’m going to enter 7,000;
followed by 19,000; 22,000; 32,000; 28,000; 20,000;
23,000; 27,000; 37,000; 40,000; 27,000 and lastly 15,000 and.. I missed the 5
there so let me go back.. Now we’re going to create the
scatter plot first. So I’m going to go 2nd Y=for STAT PLOT, 1 for
Plot 1, ENTER to turn Plot 1 ON. Then I’m going to go over to the
WINDOW and go from 0 for Xmin to 13 for Xmax and 5,000..
or let me just use 0.. 0 for Ymin and 45,000 for Ymax and the Yscl will
set at 5,000. Now when we graph we see
the scatter plot and we see that there are two local
maximums and 1 local minimum. So it does appear
that we will be able to model this data fairly
accurately with a quartic or fourth degree polynomial. So let’s compute the polynomial’s
coefficients by going STAT, right for CALC and 7 for the
quartic regression equation. Now we’ll go 2nd 1 for
L1, comma, 2nd 2 for L2 and press ENTER. And we
get the coefficients a through e: negative 58.093; 1,476.093.. oh I’m
sorry.. 1,476.099. For c: negative 12,781.019. d: 44,689.451 and e:
negative 27,906.566. Now we’re going to go to the Y=
screen and we’re going to pick up the values of a, b,
c and d and e for the quartic equation. Before doing that let me go
back to the text screen here and enter the coefficients
in the equation for y. So negative 58.093 x to the fourth plus 1,476.099 x
cubed minus 12,781.019 x squared plus 44,689.451x
minus 27,906.566. Now we’re going to go back
to the graphing calculator and we’ll do VARS 5
for STATISTICS over 2 for the EQ menu and the a
through e are the coefficients for the quartic regression
equation and so I’m going to press 2 to display
the a and then x to the power 4, plus
VARS 5, two right arrows, 3 to display the b, x cubed,
plus VARS 5, right, right, 4 for c, x squared, then plus, VARS 5
right, right, 5 to display the d, and x plus, VARS
5, right, right, 6 to display the constant
e. And now we’ll press GRAPH and there’s the quartic
function of best fit together with the scatter plot. [silence]

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