Question

Can someone tell me which is the y and which is the x

Look back at the data from the New York Marathon.
Year Competitors* Year Competitors* Year Competitors*
1976 2.1 1987 22.5 1997 31.4 2007 39.2
1977 4.8 1988 23.5 1998 32.4 2008 37.9
1978 9.8 1989 25 1999 32.5 2009 43.7
1979 11.5 1990 25.8 2000 30 2010 44.8
1980 14 1991 26.9 2001 24 2011 46.8
1981 14.5 1992 28.6 2002 32.5
1982 14.3 1993 28.1 2003 35.3
1983 15.2 1994 31.1 2004 37.3
1984 14.6 1995 29 2005 37.6
1985 16.7 1996 29 2006 38.4
1986 20.5 * in thousands

Answer 1

I would use y for the number of competitors and x for the year.

Answer 2

The slope of the best fit regression line can be found using the formula m=n(∑xy)−(∑x)(∑y)(n(∑x2)−(∑x)2.
m=n(∑xy)−(∑x)(∑y)(n(∑x2)−(∑x)2
The y-intercept of the best fit regression line can be found using the formula b=(∑y)(∑x2)−(∑x)(∑xy)(n(∑x2)−(∑x)2.
b=(∑y)(∑x2)−(∑x)(∑xy)(n(∑x2)−(∑x)2
Sum up the values of the first column of data (x).
∑x=1976+1977+1978+1979+1980+1981+1982+1983+1984+1985+1986+1987+1988+1989+1990+1991+1992+1993+1994+1995+1996+1997+1998+1999+2000+2001+2002+2003+2004+2005+2006+2007+2008+2009+2010+2011
Simplify the expression.
∑x=71766
Sum up the values of the second column of data (y).
∑y=2.1+4.8+9.8+11.5+14+14.5+14.3+15.2+14.6+16.7+20.5+22.5+23.5+25+25.8+26.9+28.6+28.1+31.1+29+29+31.4+32.4+32.5+30+24+32.5+35.3+37.3+37.6+38.4+39.2+37.9+43.7+44.8+46.8
Simplify the expression.
∑y=951.3
Sum up the values of x⋅y.
∑xy=1976⋅2.1+1977⋅4.8+1978⋅9.8+1979⋅11.5+1980⋅14+1981⋅14.5+1982⋅14.3+1983⋅15.2+1984⋅14.6+1985⋅16.7+1986⋅20.5+1987⋅22.5+1988⋅23.5+1989⋅25+1990⋅25.8+1991⋅26.9+1992⋅28.6+1993⋅28.1+1994⋅31.1+1995⋅29+1996⋅29+1997⋅31.4+1998⋅32.4+1999⋅32.5+2000⋅30+2001⋅24+2002⋅32.5+2003⋅35.3+2004⋅37.3+2005⋅37.6+2006⋅38.4+2007⋅39.2+2008⋅37.9+2009⋅43.7+2010⋅44.8+2011⋅46.8
Simplify the expression.
∑xy=1900422
Sum up the values of x2.
∑x2=(1976)2+(1977)2+(1978)2+(1979)2+(1980)2+(1981)2+(1982)2+(1983)2+(1984)2+(1985)2+(1986)2+(1987)2+(1988)2+(1989)2+(1990)2+(1991)2+(1992)2+(1993)2+(1994)2+(1995)2+(1996)2+(1997)2+(1998)2+(1999)2+(2000)2+(2001)2+(2002)2+(2003)2+(2004)2+(2005)2+(2006)2+(2007)2+(2008)2+(2009)2+(2010)2+(2011)2
Simplify the expression.
∑x2=143069406
Sum up the values of y2.
∑y2=(2.1)2+(4.8)2+(9.8)2+(11.5)2+(14)2+(14.5)2+(14.3)2+(15.2)2+(14.6)2+(16.7)2+(20.5)2+(22.5)2+(23.5)2+(25)2+(25.8)2+(26.9)2+(28.6)2+(28.1)2+(31.1)2+(29)2+(29)2+(31.4)2+(32.4)2+(32.5)2+(30)2+(24)2+(32.5)2+(35.3)2+(37.3)2+(37.6)2+(38.4)2+(39.2)2+(37.9)2+(43.7)2+(44.8)2+(46.8)2
Simplify the expression.
∑y2=29569.29011751
Fill in the computed values.
m=36(1900422)−(71766)(951.3)36(1.430694⋅1008)−(71766)2
Simplify the expression.
m=1.02955876
Fill in the computed values.
b=(951.3)(1.430694⋅1008)−(71766)(1900422)36(1.430694⋅1008)−(71766)2
Simplify the expression.
b=−2025.94956447
Fill in the values of slope (m) and y-intercept (b) into the slope y-intercept formula.

y=1.02955876x−2025.94956447

Answer 3

does that look like it would be the line of regression or does that look wrong lol

Answer 4

AHHHH so many numberssss >.>

Answer 5

i know lol , just wondering if it looks like i was doing it right lmao

Answer 6

too much math lol

Answer 7

I'm not so good with the stats ;c
Gimme few minutes, see if I can make sense of it.

Answer 8

lol im laughing

Answer 9

literally

Answer 10

this sucks butt :(

Answer 11

I don't understand this header:
Year Competitors* Year Competitors* Year Competitors*

Were there years that didn't copy paste correctly?

Answer 12

Or were years listed down the left side or something..?

Answer 13

yeah , i moved it

Answer 14

Maybe you can take picture of the problem? 0_o hmm

Answer 15

OHHH I see now... the years are mashed together next to the other column
i see i see.

Answer 16

yes lol the question asked-
Part 1: Find a regression model for this data set (1976-2011). Explain your method.1+2=3

i dont understand what it means exactly but when i put it into mathway.com that is how it solved it lol

Answer 17

Year Competitors* Year Competitors* Year Competitors*
1976 2.1 1987 22.5 1997 31.4 2007 39.2
1977 4.8 1988 23.5 1998 32.4 2008 37.9
1978 9.8 1989 25 1999 32.5 2009 43.7
1979 11.5 1990 25.8 2000 30 2010 44.8
1980 14 1991 26.9 2001 24 2011 46.8
1981 14.5 1992 28.6 2002 32.5
1982 14.3 1993 28.1 2003 35.3
1983 15.2 1994 31.1 2004 37.3
1984 14.6 1995 29 2005 37.6
1985 16.7 1996 29 2006 38.4
1986 20.5

Answer 18

Ooo there we go! :)
That' looks a lil better, yes?

Answer 19

Err I guess it depends how zoomed you are 0_o hmm

Answer 20

lol yes

Answer 21

www.mathportal.org/calculators/statistics-calculator/correlation-and-regression-calculator.php?val1=1976%2C1977%2C1978%2C1979%2C1980%2C1981%2C1982%2C1983%2C1984%2C1985%2C1986%2C1987%2C1988%2C1989%2C1990%2C1991%2C1992%2C1993%2C1994%2C1995%2C1996%2C1997%2C1998%2C1999%2C2000%2C2001%2C2002%2C2003%2C2004%2C2005%2C2006%2C2007%2C2008%2C2009%2C2010%2C2011&val2=2.1%2C4.8%2C9.8%2C11.5%2C14%2C14.5%2C14.3%2C15.2%2C14.6%2C16.7%2C20.5%2C22.5%2C23.5%2C25%2C25.8%2C26.9%2C28.6%2C28.1%2C31.1%2C29%2C29%2C31.4%2C32.4%2C32.5%2C30%2C24%2C32.5%2C35.3%2C37.3%2C37.6%2C38.4%2C39.2%2C37.9%2C43.7%2C44.8%2C46.8&ch1=expl&rb1=reg

Answer 22

thats a link for the work it showed me

Answer 23

I input a couple of different years into your equation that you ended up with.

2010:
\(\Large\rm y=1.031*2010-2028.72 = 43.58\)
We would predict about 43.58 (thousand) competitors.
Your chart shows 44.8 (thousand), so that's a really nice approximation.
1998:
\(\Large\rm y=1.031*1998-2028.72=31.22\)
We would predict about 31.22 (thousand) competitors that year.
Your chart shows 32.4 (thousand) competitors that year.

Your equation seems to work very well! :)

Answer 24

So you just put all the data in, and it did the calculations for you?
That seems smart :)

Crunching the numbers for 10 or whatever number of summations by hand would be insane.

Yah your equation makes sense, looks good!

Answer 25

I have tried setting up a linear regression model for the data on my calculator. Here is the resulting equation:
y = 1.031x - 2028.727

Answer 26

Oh wait wait I see your wall of text....
did you crunch all of that by hand? +_+ lol

Answer 27

i used a website lol

Answer 28

oh good :)

Answer 29

yes , thank goodness for technology lol :)

Answer 30

^^^^^^^^^^^^
What you said.