Question

Gonna need help with this worksheet...

Answer 1

ok here's the formula for simple regression:
Y=B0+B1*X+E
and here's the formula for multiple regression:
Y=B0+B1*X1+B2*X2+.....Bk*Xk+E

Answer 2

Can someone start me off with #1 part a?

Answer 3

@amistre64 @phi @satellite73

Answer 4

@.Sam. @jhonyy9 @lalaly @LoveYou*69 @Luis_Rivera @Mertsj @tomo

Answer 5

i have no idea how to do a least squares, or any statistics really. sorry

Answer 6

:(

Answer 7

it's kinda like slope
y=b+mx

...regression is:
y=b0+b1x

Answer 8

AMISTRE!!!!!!!!!!!!!!!!!!!!!! :DDD

Answer 9

well, one thing i know off thebat is that the anchor point for the line will be the average x and average y values

Answer 10

do you recall all the Sxx Sxy stuff? if not i can look it up to refresh

Answer 11

ditto. im just having a hard time setting up the data so it fits the regression equation.
for example, which regression equation should i use (simple or multiple)? and what do i put for B0?

Answer 12

what does Sxx and Sxy stand for again?

Answer 13

if i walk myself thru it ... they are something in the back of my head for standard errors i think

Answer 14

we want a line mx+b, such that it is the average of all the stated points, or rather that the distance squared, from the line to any given point is a minimum

Answer 15

i have SSE (sum of squares for erros) in my notes and SE (standard error of estimate)

Answer 16

those look useful

Answer 17

i also have the coefficient of determination (R^2)

Answer 18

http://stattrek.com/regression/linear-regression.aspx

thats the site i was looking for

Answer 19

hold on, im gonna upload some notes i took

Answer 20

anchor point is: \((\bar x,\bar y)\)

\[b_1=\frac{\sum[(x_i-\bar x)(y_i-\bar y)}{\sum(x_i-\bar x)}\]

so b1 is the slope and the given anchor point can be inputed into the point slope format of a line

Answer 21

forgot a square on the denominator

Answer 22

ok, nevermind about posting notes. cant get them on my computer.

Answer 23

Hours studied 2 4 5 8 10 11; avg = 6' 2/3

Exam Score 50 67 75 90 95 99 ; avg = 79' 1/3

Answer 24

2-6-2/3 = -4 2/3
4-6-2/3 = -2 2/3
5-6-2/3 = -1 2/3
8-6-2/3 = 1 1/3
10-6-2/3 = 3 1/3
11-6-2/3 = 4 1/3

50-79-1/3 = -29 1/3
67-79-1/3 = -12 1/3
75-79-1/3 = -4 1/3
90-79-1/3 = 11 2/3
95-79-1/3 = 16 2/3
99-79-1/3 = 20 2/3


((-4- 2/3)(-29- 1/3)+(-2- 2/3)(-12- 1/3)+(-1- 2/3)(-4- 1/3)+(1+ 1/3)(11+ 2/3)+(3+ 1/3)(16+ 2/3)+(4+1/3)(20+ 2/3))\((-4- 2/3)+(-2- 2/3)+(-1- 2/3)+(1+ 1/3)+(3+ 1/3)+(4+1/3))

the wolf hates me .....

Answer 25

wouldn't the 2 (xi-xbar)'s cancel out?

Answer 26

no, a sum over a sum does not cancel out like summands

Answer 27

\[\frac{a+b}{a+c}\ne\frac{b}{c}\]

Answer 28

umm, hours is "x" parts right?

Answer 29

yup

Answer 30

2 4 5 8 10 11; avg = 6' 2/3

6 12 15 24 30 33
-20
-------------------
-4 -8 -5 4 10 13

10/3 = sum (x-bar x) then

Answer 31

i have a question about the denominator. in the numerator we multiply to get the answer, but there's nothing to multiply by in the denominator, so do i just add up the answers i got for each x given subtracted by x bar?

Answer 32

o nvm i think you just answered my question ha ^^

Answer 33

-4/3
-8/3
-5/3
4/3
10/3
13/3


50 67 75 90 95 99 ; avg = 79' 1/3

150 201 225 270 285 351
-237
--------------------------
-87 -36 -12 33 48 114



-4/3( -87/3)-8/3(-36/3)-5/3( -12/3)+4/3( 33/3)+10/3( 48/3)+13/3(114/3) = 310

3(310)/10 = 3(31) = 93 as a slope?

Answer 34

6 12 15 24 30 33
-20

150 201 225 270 285 351
-237

where do these #s come from??

Answer 35

when adding or subtracting fractions, its best to multiply the whole number by the denominator, in this case that was 3 .... then you can do some normal subtracting 6 2/3 = 20/3

Answer 36

the slope should be about 5.2 .....

Answer 37

alright hold on a second. im gonna write all this out on paper and see how you got everything.

Answer 38

i forgot to square the demoninator

Answer 39

like always ;)

Answer 40

i went and let Excel do the work .... but i organized the data into what was needed

Answer 41

-4 -8 -5 4 10 13
...so these are all the answers you get when multiplying the numerators together?
-87 -36 -12 33 48 114
and
....these are all the answers when adding the denominators together?

Answer 42

4 things needed for the linear regression line

average X
average Y

sum of the products
sum of the xs squared

\[Line:~y-avgY=\frac{sum~of~products}{sum~of~xs}(x-avgX)\]

Answer 43

by hand i got a value of 10/3 .. without squareing it :)

so denominator is 100/9

Answer 44

pfft, still confused .....

Answer 45

2 4 5 8 10 11; avg = 6' 2/3

6 12 15 24 30 33
-20
-------------------
-14 -8 -5 4 10 13 , square these then add


(196+64+25+16+100+169) / 9 ... since 3^2 = 9

196
169
164
25
16
----
570

570/9 = 63 1/3

Answer 46

im not even going to attempt a product of the xy parts by hand lol

Answer 47

lol hold on im working it out on paper...

Answer 48

ok, i must be doing something wrong...
i got (300.8) / (4)
when i multiplied everything in the numerator and added in the denominator

Answer 49

\[top:~(x_1-\bar x)(y_1-\bar y)+(x_2-\bar x)(y_2-\bar y)+(x_3-\bar x)(y_3-\bar y)\\~ \\~~~~~~~~~~~~~~+(x_4-\bar x)(y_4-\bar y)+(x_5-\bar x)(y_5-\bar y)+(x_6-\bar x)(y_6-\bar y)\]

your top is worked out like this right?

Answer 50

ok, lemme type out what i wrote out...

Answer 51

( (-4&2/3 * -29&1/3) + (-2&2/3 * -12&1/3) + (-1&2/3 * -4&1/3) + (1&1/3 * 11&2/3) + ( 3&1/3 * 16&2/3) + (4&1/3 * 20&2/3) ) // ( (-4&2/3) + (-2&2/3) + (-1&2/3) + (1&1/3) + (3&1/3) + (4&1/3)

Answer 52

( ( -10/3) * -86/3) + (-4/3 * -35/3) + (-1/3 * -11/3) + (4/3 * 35/3) + (10/3 * 50/2) + (13/3 * 62/3) )
is what i did to the numerator first before multiplying and adding it

Answer 53

this worksheet says your allowed to use excel, but just not in configuring the linear regression equation ..... in other words, no letting excee process the final result.

right?

Answer 54

im assuming he just wants us to show our work.

Answer 55

lol, there is a difference between showing work, and torturing yourself.

Answer 56

its a handwritten assignment that we turn in class.

Answer 57

then it torture ...

Answer 58

YES, that class IS torture! ha

Answer 59

ok so what am i doing wrong

Answer 60

i used a graphing calc to input everything to get the answers i got

Answer 61

\[top:~(\frac{6-20}{3})(\frac{150-238}{3})+(\frac{12-20}{3})(\frac{201-238}{3})+(\frac{15-20}{3})(\frac{225-238}{3})\\~ \\~~~~~~~~~~~~~~+(\frac{24-20}{3})(\frac{270-238}{3})+(\frac{30-20}{3})(\frac{285-238}{3})+(\frac{33-20}{3})(\frac{297-238}{3})\]

\[bottom:~(\frac{6-20}{3})^2+(\frac{12-20}{3})^2+(\frac{15-20}{3})^2\\~ \\~~~~~~~~~~~~~~+(\frac{24-20}{3})^2+(\frac{30-20}{3})^2+(\frac{33-20}{3})^2\]

Answer 62

ok i didnt square each individual answer on the bottom... but for the top you dont get 300.8? want me to put it in my calc?

Answer 63

i get what i got on the excel picture i posted :)

Answer 64

for the top i get 328.67

Answer 65

thats lazy ;)

Answer 66

i know ... but im old

Answer 67

excuses excuses lol

Answer 68

you are close to it, so im sure there is just some input error in your calculator

Answer 69

i think i see it.....

Answer 70

ok i still got the wrong answer so ill just do it the way you did it... i dont know why im getting the wrong answer doing it my way

Answer 71

..cause my way is ALWAYS best ;)

Answer 72

\[top:~(\frac{-14(-88)}{9})+(\frac{-8(-37)}{9})+(\frac{-5(-13)}{9})\\~ \\~~~~~~~~~~~~~~+(\frac{4(32)}{9})+(\frac{10(47)}{9})+(\frac{13(59)}{9})\]

\[top:~\frac{-14(-88)-8(-37)-5(-13)+4(32)+10(47)+13(59)}{9}\]

\[top:~\frac{1232+296+65+128+470+767}{9}\]

\[top:~\frac{2958}{9}=328.66666.....\]

Answer 73

this was fun, but i gotta get going home now. enjoy ;)

Answer 74

yeah, it was "fun" lol
talk to you later.

Answer 75

For #1 Part B it asks what will happen if you studied 30 more minutes... so do I just plug in .5 or 1/2 to the line equation?
y=5.1895x + 44.737

Answer 76

@phi

Answer 77

http://assets.openstudy.com/updates/attachments/513fa204e4b0e549bb36e56e-amistre64-1363203876628-linearregression.jpg

Answer 78

almost. all you care about is the slope
you want the change in y (how many more points) with a change in x (hours studied)

Answer 79

so you do not care about the 44.737

Answer 80

so just plug in .5 for x and multiply by the slope?

Answer 81

Part B it asks what will happen if you studied 30 more minutes.

It is like asking, "if you move 1/2 hour on the x-axis, how far up to you move on the y-axis?"

Answer 82

yes

Answer 83

ok sounds good. thanks. i'll let you know when i need more help.

Answer 84

fyi, I checked your numbers y=5.1895x + 44.737 and they look good

Answer 85

ok so i got 21.07921567 for the standard error of estimate for Part E but I dont know how to explain if the model fits well with the data.

Answer 86

i'm also needing help with Part F
and for #2, do I basically do the same thing I did for #1 Part A first?
i'm gonna logoff, but please do continue to help if you're online and i'm not. I will log on sooner than later to see what you say.
thanks. :)

Answer 87

** i got 21.07921567 for the standard error of estimate for Part E**

How did you get this number? According to wikipedia
the standard error squared is
\[\sigma^2= \sum\frac{\epsilon \epsilon }{n-p} \]
n is the number of samples and p is 2 (# of parameters)
the residual error is the difference between the data and the least-square estimate

50 67 75 90 95 99
55.1158 65.4947 70.6842 86.2526 96.6316 101.8211

just looking at the plot, you can see it is a good fit.

Answer 88

wait, how did you get the #s below the test scores again?

Answer 89

@amistre64

Answer 90

#2 is the same concepts as #1, just a new set of numbers

Answer 91

pages relate to X, and prices to Y

Answer 92

im still working on #1 haha (parts e and f)
i was wondering where Phi got the #s underneath the test scores ^^^

Answer 93

im not sure what phis method was. youll have to consult the phi :)

Answer 94

can you help me finish parts e and f then? i have the error of estimate for e but i need to explain whether the model fits the data well. for part f i have an idea of what to do but im not 100% sure. do i draw a standard normal curve?