Question

Help please

Answer 1

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?

Answer 2

@jim_thompson5910

Answer 3

what spreadsheet program do you have?

Answer 4

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

Answer 5

I used geogebra for this graph i just attached

Answer 6

geogebra is a good choice

Answer 7

you can also use geogebra for spreadsheet work

Answer 8

Yea, so that would be negative correlation right?

Answer 9

at the top go to

view --> spreadsheet

Answer 10

we'll find out

Answer 11

oh wait, you already have the points plotted

Answer 12

Ok i did that

Answer 13

Now what?

Answer 14

in the input bar below, type

CorrelationCoefficient[

then enter the list of points surrounded by curly braces

Answer 15

So if you had points A through J, then you would have

CorrelationCoefficient[{A,B,C,D,E,F,G,H,I,J}]

Answer 16

When I press enter it erases

Answer 17

where is the algebra tab? can I see that?

Answer 18

algebra tab?

Answer 19

at the top go to

View ---> algebra

Answer 20

I'm curious to see what the point labels are

Answer 21

thx

Answer 22

for some reason, you did (0.95) twice

Answer 23

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

Answer 24

oh I see what happened

Answer 25

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

Answer 26

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

Answer 27

oh ok so it is negative correlation

Answer 28

r = -1 means we have perfect negative correlation

all of the points lie on the same line

Answer 29

but hmm not sure why i put 0.95 twice

Answer 30

the line has some negative slope

Answer 31

oh ok wait brb

Answer 32

So part A is negative correlation

Answer 33

Part B....

Answer 34

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

Answer 35

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

Answer 36

It never works when i go to the input bar

Answer 37

ok go to the CAS then

view --> CAS

Answer 38

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

Answer 39

Oh ok but your last three points are wrong

Answer 40

right, they skipped 88 for some reason

Answer 41

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

Answer 42

yea

Answer 43

so now what does the slope say once you fix that

Answer 44

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

Answer 45

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

Answer 46

that only works if you consider those two points only

Answer 47

but we have to consider all 10 points

Answer 48

which is what the FitLine function does

Answer 49

Oh ok

Answer 50

And lastly, part C

Answer 51

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

Answer 52

what do x and y represent?

Answer 53

I dont know

Answer 54

@jim_thompson5910

Answer 55

look back at the table given in the problem

Answer 56

Do you want the coordinates?

Answer 57

they define in words what x and y are

Answer 58

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

Answer 59

Oh y is the score of the math test

Answer 60

yeah

Answer 61

what does the y intercept represent?

Answer 62

I really dont know

Answer 63

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

Answer 64

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

Answer 65

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

Answer 66

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