>>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]