Question

PLEASE HELP ME ON THIS WORKSHEET!!!

Answer 1

http://assets.openstudy.com/updates/attachments/54454e65e4b02731fd672543-peyton_olson-1413828210435-thelineofbestfit.docx Heres the worksheet

Answer 2

I have absolutely no idea what to do

Answer 3

Shouldn't this be in chemistry or something? I'll still give it a look for you.

Answer 4

1/2

Answer 5

I got it in my math class

Answer 6

Oh, okay ^.^
Do you know the definitions are for independent variable and dependent variable?

Answer 7

Yeah I know that the independent variable is the mass and the dependent variable is how much it stretches

Answer 8

Im stuck on Part 3

Answer 9

do you know the linear regression? @robfozz

Answer 10

I dont think so

Answer 11

do you know the formula which gives the value of r?

Answer 12

No, sorry >.> I really have no idea what Im doing

Answer 13

as you know any measure has an uncertainty

Answer 14

huh

Answer 15

for example, what is the uncertainty of the measures of the masses applied?

Answer 16

D: I dont know

Answer 17

namely the first measure of the mass applied is 10 grams. That information is incomplete since any measures can not be accurate at 100%

Answer 18

oh ok

Answer 19

a better measure can be this:
\[m = \left( {10 \pm 1} \right)grams\]

Answer 20

where 1 grams is the uncertainty on the 10 grams

Answer 21

I dont think thats what it wants, I haven't heard of uncertainty in my entire lesson

Answer 22

I understand, do you know the least square method?

Answer 23

Yeah that sounds familiar

Answer 24

ok! Then we have to fit your data with a line whose equation is:
\[s = A + Bm\]

Answer 25

where s are the stretches, and m are the applied masses

Answer 26

But it says to use the equation b=r Sy/Sx

Answer 27

It wants me to find the slope

Answer 28

in this case we have to find the value of \[{s_x}\]

Answer 29

Yes because it gives us Sy

Answer 30

what is the formula for \[{s_x}\] ?

Answer 31

Im not sure

Answer 32

here is the formula for \[{s_x}\]:
\[{s_x} = \sqrt {\frac{1}{N}\sum\limits_{i = 1}^N {{{\left( {{m_i} - \bar m} \right)}^2}} } \]
where N is the number of the measures of the applied masses m_i, and \[{\bar m}\] is the mean value of the measures m_i

Answer 33

oh yeah, I remember that now

Answer 34

first you have to compute the value of \[{\bar m}\]

Answer 35

what is \[{\bar m}\]?

Answer 36

10?

Answer 37

please remember this formula:
\[\bar m = \frac{{\sum\limits_{i = 1}^N {{m_i}} }}{N} = \frac{{{m_1} + {m_2} + {m_3} + {m_4} + {m_5}}}{5} = ...?\]

Answer 38

oooooooooh Is it 12?

Answer 39

are you sure?

Answer 40

Oh, no actually

Answer 41

hint:
\[\frac{{{m_1} + {m_2} + {m_3} + {m_4} + {m_5}}}{5} = \frac{{10 + 20 + 30 + 40 + 50}}{5} = ...?\]

Answer 42

30!

Answer 43

ok!

Answer 44

now we have to compute these quantities:
\[\begin{gathered}
{\left( {10 - 30} \right)^2} = ...? \hfill \\
{\left( {20 - 30} \right)^2} = ...? \hfill \\
{\left( {30 - 30} \right)^2} = ...? \hfill \\
{\left( {40 - 30} \right)^2} = ...? \hfill \\
{\left( {50 - 30} \right)^2} = ...? \hfill \\
\end{gathered} \]

Answer 45

-890
-880
-870
-860
-850

Answer 46

Arent thoe squares supposed to be on the outside?

Answer 47

If they are then
400
100
0
100
400

Answer 48

@Michele_Laino

Answer 49

@Michele_Laino

Answer 50

ok!

Answer 51

now we have to add those quantities, namely:
\[400 + 100 + 0 + 100 + 400 = ...?\]

Answer 52

1000

Answer 53

next we have to divide 1000/ by 5

Answer 54

200

Answer 55

ok!

Answer 56

now we have to compute this:
\[\sqrt {200} = ...?\]

Answer 57

uhhhhh

Answer 58

what is \[\sqrt {200} = ...?\]

Answer 59

14.14?

Answer 60

ok!

Answer 61

that's the value of \[{s_x}\]

Answer 62

Should I round it to just 14?

Answer 63

since s_y=7.32, I think that it is better to write s_x as 14.14

Answer 64

ok

Answer 65

now you can compute the b coefficient

Answer 66

b=0.51?

Answer 67

ok!

Answer 68

So that would be the answer?

Answer 69

yes! b= 0.51

Answer 70

Awesome! Thank you so much! I hate to bug you for such a long time but could you help me with the next part too?

Answer 71

ok!

Answer 72

Thanks

Answer 73

we have to compoute a?

Answer 74

oops...compute*

Answer 75

We have to find the Y intercept using that formula

Answer 76

we can use the first pair of your measures, namely mass m= 10 grams, and stretch = 5.8 cm, in other words, we have to compute this:
\[y - bx = 5.8 - 0.51 \times 10 = ...?\]

Answer 77

Im not sure what A is but the answer to your other question is 0.7?

Answer 78

ok! We can assume a=0.7

Answer 79

in this case the y-intercept is the value of y when x=0, so, what is the y intercept?

Answer 80

Is it 0.7 still?

Answer 81

yes!

Answer 82

it is easy, now, to write the requested equation, what is it?

Answer 83

okay so is that the y intercept as well?

Answer 84

yes! the y-intercept is 0.7, namely it is equal to the coefficient a

Answer 85

okay so a is also 0.7

Answer 86

yes!

Answer 87

even if that's not an exact value, since also the coefficient "a" has an uncertainty

Answer 88

So what does Step 3 want now?

Answer 89

we have to write the equation of our function, using the variables m and s, and the coefficients a and b

Answer 90

What was m and s again?

Answer 91

m= mass, and s= stretch

Answer 92

Oh nevermind, so how do I write the equation

Answer 93

it is simple, starting from the equation:
y = a+bx,
we have to replace y, and x with s and m, and we have to set a = 0.7 and b=0.51

Answer 94

What numbers are x and y

Answer 95

they aren't numbers now

Answer 96

they are two variables

Answer 97

So the equation is just y=0.7+0.51x