Question

The table below shows the distance y, in miles per minute, of a toy car at different times x, in minutes:

Time (x)
(minutes) 10 20 30 40
Distance (y)
(miles) 0.2 0.8 0.1 0.4

Part A: What is the most likely value of the correlation coefficient of the data in the table? Based on the correlation coefficient, describe the relationship between time and distance of the toy car. (4 points)
[Choose the value of correlation coefficient from −1, 1, −0.04, 0.99]

Part B: What is the value of the slope of the graph of distance versus time between 10 minutes and 20 minutes, and what does the slope represent? (3 points)

Part C: Does the data in the table represent correlation or causation? Explain your answer. (3 points)

Answer 1

HERO!! YEW ES HERE PLEASE HELP MEEEEEE T~T

Answer 2

Can you screenshot the question please?

Answer 3

Okay, so, 1st question is, have you attempted to graph these data points? The best online graph to use for this is http://www.desmos.com

Answer 4

ok what do i do once i have the site i dont know what im suppose to graph

Answer 5

You graph the given table of (x,y) points.

Answer 6

ok ill try

Answer 7

^^so it looks like this

Answer 8

Okay, so based on that, what is the value of the correlation coefficient? Is the value of the correlation coefficient close to zero or one?

Answer 9

Closer to zero because that makes a straight line

Answer 10

?

Answer 11

Correct. So which of the given values for the correlation coefficient is close to zero?

Answer 12

0.1

Answer 13

now what

Answer 14

I should ask you, what are the given values of the correlation coefficient they are asking you to choose from?

Answer 15

−1, 1, −0.04, 0.99

Answer 16

its not 1

Answer 17

its not -1

Answer 18

Which of those values are closest to zero?

Answer 19

and its not 0.99 so it has to be -0.04 right

Answer 20

Correct.

Answer 21

ok so what would be next

Answer 22

Next you have to calculate the slope using values for the first two columns of the table.

Answer 23

so 10 and 20 and 0.2 and 0.8?

Answer 24

how would i calculate that? 10 - 20 over 0.2 - 0.8

Answer 25

@Hero

Answer 26

You should actually make it so that when you subtract you end up with positive numbers. In other words subtract the smaller numbers from the bigger numbers.

Answer 27

im confused i thought that what i did

Answer 28

so it would be 10-0.2 and 20-0.8?

Answer 29

What you've done now is mix up the x's and y's. You subtract y's from y's and x's from x's.

Answer 30

im confused

Answer 31

before i put y-y and x-x but u said u have to do smaller - bigger so i gave you smaller - bigger

Answer 32

can you show me an example please cause i really am confused rn

Answer 33

@Hero

Answer 34

All you had to do was swap the order of the y's and x's, not mix them up.

Answer 35

ok

Answer 36

so 20-10 and 0.8-0.2?

Answer 37

There you go

Answer 38

ok so its 10 and 0.4

Answer 39

Yeah, but you have to simplify that because what you actually have is \(\dfrac{10}{\dfrac{4}{10}}\)

Answer 40

\(0.4\) and \(\dfrac{4}{10}\) both mean four-tenths. One is in decimal form the other is in fraction form.

Answer 41

10 over 4 over ten = 25 when simplified

Answer 42

@Hero

Answer 43

Just to let you know there are 3 more questions i need help on after dis if thats okie e.e

Answer 44

It's \(10 \div \dfrac{4}{10}\) or \(10\) divided by \(\dfrac{4}{10}\) but yeah 25 is correct.

Answer 45

So what does that mean in terms of the slope?

Answer 46

urm it means that the slope is 25?

Answer 47

Correct.

Answer 48

so after we find the slope now what

Answer 49

what i have so far


Part A: The correlation coefficient to the data is -0.04 Because its the closest to zero.

Answer 50

... because the graph of the given data suggests that the correlation coefficient is close to zero.

Answer 51

Ohhh ok that makes more since

Answer 52

Whoops, I deleted the wrong thing. Can you re-post that?

Answer 53

This?
Part A: The correlation coefficient to the data is -0.04 Because its the closest to zero.

Answer 54

@Hero This is what u wanted?

Answer 55

No you posted something else after that. I deleted it accidentally.

Answer 56

Based on the correlation coefficient, describe the relationship between time and distance of the toy car.

Answer 57

Dis?

Answer 58

@Hero x'D yew still there

Answer 59

So basically, the correlation coefficient is a way of measuring the strength of relationship between two variables. Values close to one indicate a strong positive relationship. Values close to negative one indicate a strong negative relationship. Values close to zero indicate no relationship. That's your hint.

Answer 60

The relationship between these variables is a No relationship because its closer to zero

Answer 61

^^^If this is correct den were on to Part B:

Answer 62

The slope equals 25. This represents the time it takes for the toy car to hit its maximum?

Answer 63

One moment.

Answer 64

Do you know the slope formula?

Answer 65

If so, then what is it?

Answer 66

y=mx+b?

Answer 67

i thought we already did the slope tho

Answer 68

That's the equation of a line, not the slope formula.

Answer 69

den i gots no clue

Answer 70

I went with the information you provided because I assumed you knew the slope formula

Answer 71

its been a while

Answer 72

\(m = \dfrac{y_2 - y_1}{x_2 - x_1}\). If you don't know it, you should have looked it up.

Answer 73

The y values go in the numerator, x values in the denominator.

Answer 74

i did e.e

Answer 75

No, you did the reverse of what I just said above.

Answer 76

\(\color{#0cbb34}{\text{Originally Posted by}}\) @AnimeGhoul8863
how would i calculate that? 10 - 20 over 0.2 - 0.8
\(\color{#0cbb34}{\text{End of Quote}}\)

Answer 77

That's the proof you put x values over y values

Answer 78

so i use that for the slope?

Answer 79

im so confused

Answer 80

why are we doing the slope all over agian we already figured it out

Answer 81

it equals 25

Answer 82

Are you not understanding that the slope is wrong because you put x values over y values when the slope formula suggests to put the y values over the x values?

Answer 83

What are you talking about

Answer 84

\(\color{#0cbb34}{\text{Originally Posted by}}\) @AnimeGhoul8863
urm it means that the slope is 25?
\(\color{#0cbb34}{\text{End of Quote}}\)
\(\color{#0cbb34}{\text{Originally Posted by}}\) @Hero
Correct.
\(\color{#0cbb34}{\text{End of Quote}}\)

Answer 85

Yep, and that is wrong for reasons I already mentioned. You'll have to re-calculate it.

Answer 86

can you give me an example of what you mean cause your really not making since rn

Answer 87

Example:
x = {2, 4}
y = {3, 6}

Calculate slope

Slope formula is \(m = \dfrac{y_2 - y_1}{x_2 - x_1}\)

You did the equivalent of this when calculating the slope:

\(m = \dfrac{4 - 2}{6 - 3} = \dfrac{2}{3}\)

You put the x values in the numerator and the y values in the denominator when in fact the correct slope is this:

\(m = \dfrac{6 - 3}{4 - 2} = \dfrac{3}{2}\)

Answer 88

\[\frac{ 20-10 }{ 0.8-0.2 }\]?????

Answer 89

That's not correct.

Answer 90

Put the y values in the numerator and the x values in the denominator.

Answer 91

\[\frac{ 0.8-0.2 }{ 20-10 }\]????????

Answer 92

Finally...

Answer 93

im sorry but this confuses me extremely easily

Answer 94

Sorry to hear that.
\(\dfrac{\dfrac{6}{10}}{10}\) is what we have now or \(\dfrac{6}{10} \div 10\)

Answer 95

are we looking for exact form or decimal form?

Answer 96

I have to go after this so basically \(\dfrac{6}{100}\) is close to a zero slope. In order to make any sense out of this we need to force the denominator to equal one. The only way to do that is to multiply top and bottom by \(\dfrac{1}{100}\)

Answer 97

When we do that we get \(\dfrac{\dfrac{6}{100}}{1}\) or \(\dfrac{0.06}{1}\) So the slope means that for every minute the toy car travels, it only travels a distance of six hundredths of a mile.

Answer 98

Which makes sense since it is a toy car. We wouldn't expect it to travel far in a minute.

Answer 99

so the slope Equals 0.06 ok that makes since