Question

A student is assessing the correlation between the average number of hours of internet browsing and average score on a math test for the students of a class. The table below shows the data:


Number of hours of internet browsing
(x) 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5
Score on math test
(y) 95 94 93 92 91 90 89 87 86 85


Part A: Is there any correlation between the average number of hours of internet browsing and average score on the math test for the students of the class? Justify your answer. (4 points)

Answer 1

Part B: Write a function which best fits the data. (3 points)

Part C: What does the slope and y-intercept of the plot indicate? (3 points)

Answer 2

Have you found the deviations in x and in y?

Answer 3

(doesn't matter whether n-1 or n)

Answer 4

No I havent done anything, Im very confused

Answer 5

Do you know about "standard deivation" though?

Answer 6

I think so

Answer 7

In your shoes I'd graph the data first. That would give you an instant visual indication of whether the input and output are correlated. If you agree, go ahead with a dot plot.

Answer 8

There are several equivalent formulas for calculating "correlation" (or "correlation coefficient"). Please find and share one (particularly if there is one that is reasonably clear to you).

Answer 9

Um ok

Answer 10

The line of best fit, is in the form of

\(\color{#000000 }{ \displaystyle y=\left(r\frac{S_y}{S_x}\right)x+\left[\bar{y}-\left(r\frac{S_y}{S_x}\right)\bar{x}\right] }\)

going through the point \((\bar{x},\bar{y})\).

source for correlation coeffieitn r
https://www.mathsisfun.com/data/correlation.html

Answer 11

\(S_x\) is deviation in X, and \(S_y\) is deviation in Y.

Answer 12

Note that some instructors allow use of sophisticated calculators, such as the TI-83, for finding the correlation coefficient, r.

Answer 13

Solomon: "standard deviation," not just "deviation."

Answer 14

I am using short hand, sorry...

Answer 15

Our goal is maximum clarity for the student, so let's write everything out.

Answer 16

This is all very confusing

Answer 17

But continue

Answer 18

Yes

Answer 19

Lexi, all we're asking is that you look for formulas for calculating the correlation coefficient, r. Have you studied "correlation coefficient" yet? Solomon and I could each suggest a formula, but to me it's more important that YOU know where to find such formulas and that y ou actually pick one.

Answer 20

Yes, cant I just look at the graph though?

Answer 21

if its going up its positive, down negative, scattered none

Answer 22

well, some people roughly sketch it from the graph, and that perhaps is what you are asked to do, but I never go via this kind of approach. because, this is guessing rather than solving.

Answer 23

Solving is rather confusing

Answer 24

I have to get this done though

Answer 25

I'm sorry you find this confusing. Focus on one thing at a time. That one thing is "Correlation coefficient." hold the other topics for later, please.

Again, Lexi, I ask you to find a formula for r, the correlation coefficient, and share it with
Solomon and me.

Answer 26

Solomon gave up lol

Answer 27

but, I learned something to do with y1 + y2/ x2+x1

Answer 28

Lexi, please let's stick to topic. I very much doubt that Solomon has given up.
We've got to stick to topic, with no asides about solomon, about how confusing this is, or the like.

Answer 29

I need for you to find an exact, detailed formula for r, the correlation coeff, "I learned something to do with so and so " is not helpful.

Answer 30

ok, i will find it give me a few mins

Answer 31

Step 1: Find the mean of x, and the mean of y
Step 2: Subtract the mean of x from every x value (call them "a"), do the same for y (call them "b")
Step 3: Calculate: a × b, a2 and b2 for every value
Step 4: Sum up a × b, sum up a2 and sum up b2
Step 5: Divide the sum of a × b by the square root of [(sum of a2) × (sum of b2)]

Answer 32

this is off the site

Answer 33

yes, good :)

Answer 34

that is understandable, right?

Can you find the mean for X ?

Answer 35

Would you follow these steps, please? I don't care where y ou get your formula; what I do care about is the accuracy and the relevancy of y our formula.
Any questions about this formula?

Answer 36

This is a lot more understandable, the mean is everything added, then / by the # of #

Answer 37

correct?

Answer 38

yes

Answer 39

So for the mean in the x-value (or "X-list"), add all the x-values, and divide by the # of the values.

Answer 40

I am temporarily withdrawing from this conversation. If you need me, tag me.

Answer 41

ok

Answer 42

give me a minute to get that please

Answer 43

sure

Answer 44

2.25

Answer 45

Yes, (the mean in X is often denoted as \(\bar{x}\), so if you don't mind I will write....)

\(\bar{x}=2.25\).

Answer 46

ok

Answer 47

Now, can you find the mean in Y?

Answer 48

yes, again 1 minute

Answer 49

(add all Y's and divide by how many Y's there are)

Answer 50

take your time..

Answer 51

90.2

Answer 52

yes, and that is correct....

So we can write the mean for Y as;
\(\bar{y}=90.2\)

((I'm introducing these notations because they are useful... if not now, then later))

Answer 53

ok

Answer 54

In any case, now let's refer to the \(x\)-list.

(x-list)
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5

Answer 55

They both are functions right?

Answer 56

subtract the mean in x (the 2.25) from each of these values, and respectively record what you get...

Answer 57

time out
what do you mean by this question?

Answer 58

the sets of data, x and y

Answer 59

Well, when it comes to correlation, we treat each \(x\) and \(y\) as [discrete] functions.

Answer 60

ok

Answer 61

time in

Answer 62

will again refer to the \(x\)-list.

(x-list)
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5

subtract the mean in x (the 2.25) from each of these values,
and respectively record what you get...

Answer 63

so your asking like 0- 2.25

Answer 64

yes, like that, and so on for each value in the x-list...

Answer 65

-2.25
-1.75
-1.25
-0.75
-0.25
0.25
0.75
1.25
2.25

Answer 66

Yes, so we can, so far, say ...


(x-list) "a"

0 -2.25
0.5 -1.75
1 -1.25
1.5 -0.75
2 -0.25
2.5 0.75
3 0.25
3.5 1.75
4 1.25
4.5 2.75

Answer 67

Now, let's refer to the y-list,

y-list "b"

95
94
93
92
91
90
89
87
86
85

Answer 68

we had the mean for y,
\(\bar{y}=90.2\)

So to find the b's, subtract 90.2 from each value in the y-list.

Answer 69

I think I got Part A already

Answer 70

Its negative correlation

Answer 71

how do you know the correlation is negative?

because x increases and y decreases?

Answer 72

Yes

Answer 73

Alright, good...

Do you want to find the correlation coefficient precisely though, or ... ?

Answer 74

No, we've been on Part A for an hour, I need to get this done

Answer 75

Sure ... but, in any case, you got that link to refer to if you need to find the correlation coefficient ...

Answer 76

G☼☼D LUCK!

Answer 77

OK part B

Answer 78

Part B: Write a function which best fits the data. (3 points)

Answer 79

and for that we will need to continue what we have been doing

Answer 80

Now, let's refer to the y-list,

y-list "b"

95
94
93
92
91
90
89
87
86
85

we had the mean for y,
\(\bar{y}=90.2\)
So to find the b's, subtract 90.2 from each value in the y-list.

Answer 81

95 - 90.2

and on...

Answer 82

yes every time the grade goes up by one point the person spent half hour less on internet good luck:)

Answer 83

kk
4.8
3.8
2.8
1.8
0.8
-0.2
-1,2
-3.2
-4.2
-5.2

Answer 84

There

Answer 85

Functions are f(x)= mx+b=c correct

Answer 86

So far we have.... (btw, you did make some mistakes, I corrected, you are on the right track overall)

x-list y-list "a" "b"

0.0 95 -2.25 4.8
0.5 94 -1.75 3.8
1.0 93 -1.25 2.8
1.5 92 -0.75 1.8
2.0 91 -0.25 0.8
2.5 90 0.25 -0.2
3.0 89 0.75 -1.2
3.5 87 1.25 -2.2
4.0 86 1.75 -3.2
4.5 85 2.25 -4.2

Answer 87

ok

Answer 88

Now, you have to find all a×b
and to respectively record them

like, (-2.25) × 4.8

Answer 89

There has to be a simpler way to do this, I just need a function.

Answer 90

A precise function is that difficult.... (you can use a calculator to calculate the regression line, but the actual steps are as hard as that)

Answer 91

This, like most of the stuff in statistics is ridiculously long, although each step individually is doable.

Answer 92

I dont need it to be precise, I just need like the slope and a plus , f(x)= mx+ b=c

Answer 93

yes, and those steps I want you to preform is the part of mx+b

Answer 94

unless, you want to graph the points, and just visualize the line of best fit...

Answer 95

yes

Answer 96

that is certainly easier, but that is not going to give you the precise slope and y-intercept.

Answer 97

Thats ok

Answer 98

That was how i was taught to do it