Help please

- anonymous

Help please

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- anonymous

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:
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.
Part B: Write a function which best fits the data.
Part C: What does the slope and y-intercept of the plot indicate?

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- anonymous

@jim_thompson5910

- jim_thompson5910

what spreadsheet program do you have?

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- anonymous

Ok so I made my own graph for part A and I found that it has a negative correlation, right?

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- anonymous

I used geogebra for this graph i just attached

- jim_thompson5910

geogebra is a good choice

- jim_thompson5910

you can also use geogebra for spreadsheet work

- anonymous

Yea, so that would be negative correlation right?

- jim_thompson5910

at the top go to
view --> spreadsheet

- jim_thompson5910

we'll find out

- jim_thompson5910

oh wait, you already have the points plotted

- anonymous

Ok i did that

- anonymous

Now what?

- jim_thompson5910

in the input bar below, type
CorrelationCoefficient[
then enter the list of points surrounded by curly braces

- jim_thompson5910

So if you had points A through J, then you would have
CorrelationCoefficient[{A,B,C,D,E,F,G,H,I,J}]

- anonymous

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- anonymous

When I press enter it erases

- jim_thompson5910

where is the algebra tab? can I see that?

- anonymous

algebra tab?

- jim_thompson5910

at the top go to
View ---> algebra

- jim_thompson5910

I'm curious to see what the point labels are

- anonymous

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- jim_thompson5910

thx

- jim_thompson5910

for some reason, you did (0.95) twice

- jim_thompson5910

delete point A then do CorrelationCoefficient[{B,C,D,E,F,G,H,I,J,K}]

- jim_thompson5910

oh I see what happened

- jim_thompson5910

do you see the lower case letters a though g? how they're all -1
those are the results of you typing in CorrelationCoefficient[{A,B,C,D,E,F,G,H,I,J}]
so the correlation coefficient is -1

- jim_thompson5910

now that I think about it, it might be better to do this sort of command in the CAS

- anonymous

oh ok so it is negative correlation

- jim_thompson5910

r = -1 means we have perfect negative correlation
all of the points lie on the same line

- anonymous

but hmm not sure why i put 0.95 twice

- jim_thompson5910

the line has some negative slope

- anonymous

oh ok wait brb

- anonymous

So part A is negative correlation

- anonymous

Part B....

- jim_thompson5910

in the input bar, type
FitLine[{A,B,C,D,E,F,G,H,I,J}]
and an equation of the line will pop up in the algebra tab

- jim_thompson5910

or you can pick any two points and find the slope, then use y = mx+b

- anonymous

It never works when i go to the input bar

- jim_thompson5910

ok go to the CAS then
view --> CAS

- jim_thompson5910

type FitLine[{A,B,C,D,E,F,G,H,I,J}] into the CAS

- anonymous

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- jim_thompson5910

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- anonymous

Oh ok but your last three points are wrong

- jim_thompson5910

right, they skipped 88 for some reason

- anonymous

It should be (3.5,87) and (4,86) and (4.5,85)

- anonymous

yea

- anonymous

so now what does the slope say once you fix that

- jim_thompson5910

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- jim_thompson5910

the correlation coefficient r is no longer -1 exactly, but it's still pretty close

- anonymous

I went to mathway and it said this,....

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- jim_thompson5910

that only works if you consider those two points only

- jim_thompson5910

but we have to consider all 10 points

- jim_thompson5910

which is what the FitLine function does

- anonymous

Oh ok

- anonymous

And lastly, part C

- anonymous

Well the slope is -2.25 and the y intercept is 95.27... but what does it indicate?

- jim_thompson5910

what do x and y represent?

- anonymous

I dont know

- anonymous

@jim_thompson5910

- jim_thompson5910

look back at the table given in the problem

- anonymous

Do you want the coordinates?

- jim_thompson5910

they define in words what x and y are

- jim_thompson5910

x = number of hours browsing the internet
y = ???

- anonymous

Oh y is the score of the math test

- jim_thompson5910

yeah

- jim_thompson5910

what does the y intercept represent?

- anonymous

I really dont know

- jim_thompson5910

it's where the x coordinate is 0 right? basically where the graph crosses the y axis

- jim_thompson5910

the y-intercept of the regression line is where the predicted score would be if you spend no time on the internet
ie, if you spend no time on the internet, then it is predicted you get a score of 95.27

- jim_thompson5910

the slope tells us how the score changes as x changes
each time the number of hours browsing the internet goes up by 1, the predicted score goes down by about -2.25

- anonymous

Thank you! Thank you! Thank you!!!!!

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