Question

The table shows the number of search and rescue cases handled by the U.S. Coast Guard from 2000 to 2006.
Which equation represents the best fit line for the data? Assume x represents the number of years since 2000
(so, for 2006, x = 6).

Answer 1

Those are ugly numbers, but take the first and last set as (x,y) pairs
can you find the equation of a line given two points?

Answer 2

11891 x + 6 y = 24023284

Answer 3

First, notice that the question says
Assume x represents the number of years since 2000

so you have to relabel the x values as 0,1,2, ... 6

the first point is (0, 40214)
the last point is (6, 28323)

do you know how to find the slope?

Answer 4

y1-x1/y2-x2?

Answer 5

slope is change in y divided by change in x

Answer 6

rise/run?

Answer 7

yes. but can you find the slope for the 2 points

(0, 40214)
(6, 28323)

Answer 8

y2-y1/x2-x1?

Answer 9

yes if you mean (x1,y1) is the first point and (x2,y2) is the 2nd point

Answer 10

When you have time, this might help
http://www.khanacademy.org/math/algebra/linear-equations-and-inequalitie/slope-and-intercepts/v/slope-of-a-line

Answer 11

ok. is the slope-1981.83?

Answer 12

yes. btw, your first equation is almost right, except for the number on the right side

but your choices are in slope-intercept form, so it makes sense to find the slope and y-intercept.

the y intercept is the value of y when x is 0. In this case, they tell us.

so you can write the equation as
y = -1982 x + ??

any idea what the y-intercept is?

Answer 13

40214??

Answer 14

But after looking at the choices, both (a) and (d) are close (too close)

So it looks like they want you to figure out the *best* fit Have you learned how to do that?

Answer 15

no...

Answer 16

Did the teacher ever explain how to do this problem?

Answer 17

nope

Answer 18

what class is this? what grade?

Answer 19

advanced algebra

Answer 20

Here is the procedure
http://faculty.cs.niu.edu/~hutchins/csci230/best-fit.htm

it is a bit complicated.

Answer 21

First step is add up all the x values 0+1+...+6 = 21

Answer 22

and add up all the y values. what do you get?

Answer 23

238,713

Answer 24

so far we have sumx= 21 and sumy= 238713
now we need the sum of the squares of x (square each number and add up)

Answer 25

90

Answer 26

I got 91

Answer 27

oops i forgot the one..

Answer 28

sumx= 21 , sumy= 238713, sumx2= 91

now we need the sum of x*y (multiply x times y of each pair and add up)

Answer 29

656926

Answer 30

ok we now have
sumx= 21 , sumy= 238713, sumx2= 91, sumxy= 656927
and we have ct= 7 values

now we find
XMean = SumX / Count
and YMean= sumy/count

Answer 31

3 and 34101.86

Answer 32

now (finally)
Slope = (SumXY - SumX * YMean) / (SumX2 - SumX * XMean)

Answer 33

-713.68?

Answer 34

no. better do it step by step. what do you get for the top?

btw, this can be done by some calculators. Are you supposed to have learned how to use a calculator to do this?

Answer 35

the top is
(SumXY - SumX * YMean)
656927-21*34101.86)

Answer 36

i haven't learned yet. For the top I got -59212.06 the first time

Answer 37

looks good for the top

now the bottom
SumX2 - SumX * XMean

Answer 38

28?

Answer 39

yes, now slope
m= -59212.06/28

Answer 40

-2144.72

Answer 41

-2114.72

Answer 42

i typed it wrong the first time

Answer 43

looks good, that rounds to -2115

finally
YInt = YMean - Slope * XMean

Answer 44

40446.86

Answer 45

close enough. Choice (d)

If I were in a hurry, I would have use the slope estimate we first found (using the first and last points) to narrow the choices to (a) or (d). Then I would say (a) has a y-intercept of exactly the first entry, and chances are the *best fit* line will not (how lucky could we be?). That leaves (d)

Answer 46

But I doubt they want you to memorize all those steps (does any of this look familiar?)

Answer 47

alright. Thanks so much for your help

Answer 48

it looks a little familiar