Question

This really makes no sense at all. I don't even understand why they would ask this

Answer 1

They didn’t put any points on this picture, nor did they tell what the coordinates were. All I can tell is that is is a negative correlation.

Answer 2

@mathmale
Look at this. Does this make sense to you?

Answer 3

Hello!
To answer your question: yes.
Stand back from the illustration a bit and try to describe how the dependent variable y seems to be behaving as the independent variable x increases.

Answer 4

All that is asked for is a qualitative response (no numbers required).

Answer 5

To be honest, I don't really understand how to answer that question besides, "As x goes on, y goes downward in a negative slope".

Answer 6

I'll respond with a more familiar example: y = -x + 2.
Supposing that x increases, how does y respond?

Answer 7

As x increases, y decreases

Answer 8

Your statement is basically correct, 'though it could be polished up to read
"As x goes on, y goes downward, and therefore the slope is negative".
this is a problem from statistics in which we're trying to determine how to variables are related to each other.

Answer 9

Okay, so how would I find the answer to the initial statement? Would it be y = -x + 2? Or was that just an example?




And by the way, I just figured out that I can use Microsoft Excel as a graphing calculator. I just did a whole assignment by myself and found the correlation coefficients, equations, and functions to different graphs and charts. It was awesome to say the least.

Answer 10

cLOSELY related to this discussion is the concept of "correlation."

You and I need to discuss that concept in depth.

Because your data (in the given graph) appears to be decreasing with x (that is, y decreases when x increases/moves to the right), we say that the correlation between x and y is negative in this case.

Answer 11

Suggest you make up a review sheet with vocabulary such as "correlation," "correlation coefficient," etc., along with definitions and examples. I'd be glad to help with that.

Answer 12

"Okay, so how would I find the answer to the initial statement? Would it be y = -x + 2? Or was that just an example?"

Whose initial statement? Mine, that of the homework problem, or yours?

If confronted with that data plot, I'd write the following:

"The scatterplot of data demonstrates that as x increases, y consistently decreases, and therefore the correlation coefficient is negative."

Later you 'll recognize that because the data is in fact widely scattered, not neatly arranged along a straight line, the correlation coefficient would not be close to -1, but would be more like -.5 or -.6. Don't worry about this until you are required to discuss strength of correlation.

Answer 13

Okay, I can do that. But I have a question regarding a question.

Answer 14

Write a polynomial function for the data.

Year 1957 , 1967, 1977, 1987, 1997, 2007
Retail Space (Billion Ft^2) 2.8 6.7 1 4.7 27.3 44.9 67.9

Would that polynomial be y = 0.1262x + 0.955?
@mathmale

Answer 15

First of all, please identify the type of model you're using here.
We discussed three types earlier;

LINEAR
QUADRATIC
EXPONENTIAL
(THERE ARE OTHERS)

Answer 16

Square feet.

Answer 17

Here, time is the independent variable; retail space availability is the dependent variable.

Answer 18

So it would be i the format of y = ae^(bx) wouldn't it?

Answer 19

y = 0.1262x + 0.955 is indeed a polynomial.

We worked a problem involving an exponential model earlier today. Do you remember how we identified the data as fitting an expo model?

Answer 20

Write a polynomial function for the data.

Year 1957 , 1967, 1977, 1987, 1997, 2007
Retail Space (Billion Ft^2) 2.8 6.7 1 4.7 27.3 44.9 67.9

Would that polynomial be y = 0.1262x + 0.955?

The problem answers my question regarding which model to use: polynomial. Ignore exponential models for now.

Answer 21

You ask me, "Would that polynomial be y = 0.1262x + 0.955?" I'm reluctant to answer without knowing first how you obtained that polynomial (which, incidentally, is a linear function.

Answer 22

Yes, It is a linear function. I plotted the data and then found a line of best fit. And that is the equation for the line of best fit. I knew that it was a polynomial (which is why I asked), but I did not know if it was THE polynomial I needed o answer this question correctly.

Answer 23

Personally, I'd make up a table such as those presented to you in earlier problems that we worked on. I'd let x=0 represent 1957, x=2 1967, x=3 1977, and so on.

Answer 24

I'd have to do all the work myself in order to judge your equation correct or incorrect. I'd be most interested in seeing how you obtained that result. Only you can decide whether it's worth the time and effort to photograph your work and share it with me or better to move on to another problem.

Answer 25

I used Microsoft Excel, I plotted the points onto a graph and it automatically gave me the line of best fit. It is just like a graphing calculator.

Answer 26

Also, Ricky, you could check your own equation by choosing one point at random from the given data, substituting that data into the linear model, and determining whether or not the resulting equation is true.

Answer 27

Okay! let me do that real quick.

Answer 28

Aha. A pic is worth a thousand words. What you are doing, my friend, is "regression analysis." In other words, you are fitting a line to given data and coming up with the eqution of that line. All of that info I got from one quick glance at your graph.

Answer 29

Was the data given to you, or was it the image y ou've just shared that was given to y ou in this problem?

Answer 30

I used Microsoft Excel, I plotted the points onto a graph and it automatically gave me the line of best fit. It is just like a graphing calculator. SO COOL that you have this tool and know how to use it!

Answer 31

So what kind of info do you need from me right now?

Answer 32

I just had an image of a chart with numbers. I had to graph it and find a polynomial equation that described it. I just plotted the points and it gave me a line, so I thought that that would be it. I decided to ask you before I made a clear decision

Answer 33

If you asked me whether your equation is "right" or not, I'd put your data into my calculator and command the calculator to give me the equation of the regression line in return.

When you have more experience you'll be able to tell pretty quickly just by looking at the graph (the one you've shared)

Answer 34

whther or not your regression line is correct or not.
Notice that your line aligns pretty well with your data points, and that some points are on one side of the line whereas others are n the other side.

So there
s and excellent chance tht your result is correct.

Answer 35

I thought that it'd be right, considering that it was the line of best fit.

Answer 36

You used Excel (an appropriate tool) appropriately, and have produced a beautiful graph including both a scatter plot of the data and the regression line stemming from your data.

In this case I'd be far more impressed with yo ur evident abililty to do this than I would be by a "right" answer.

Answer 37

Yes. You need to develop a sense of what constitutes an appropriate "answer" or "result."
You were correct in concluding that this line was the "best fit" to the data given. Exactly right train of thought.

Answer 38

so would

y = 0.1262x + 0.955

be the polynomial function that I would need in order to describe this set of data? That is the real question here.

Answer 39

Yes. You've fitted a straight line approximation (better known as regression line) to the given data. Yes, that str. line describes your data moderately well; it is not a perfect fit, but a good one. Note that YOU are not at fault if the line describes the data only "moderately well;" the fact is that the data doesn't precisely lie on a single straight line, although it does lie close to that line.

Answer 40

Regression lines are almost always just approximate models for the data you're analyzing.

Answer 41

Yes, my lessons said that if it is closer to -1 it has a tighter line rather than a line close to one? That's all I can remember.

Answer 42

It was something like that.

Answer 43

The closer your data is to the line, the greater the MAGNITUDE of the correlation coeff.
If all of your data points were actually sitting on the line, your correl. coeff. would be +1 in this case.

Answer 44

Oh, yes, that makes a lot more sense! Thank you!

Answer 45

In the previous example we've discussed, the correlation was negative because y decreased when x increased, and the data was not very close to the line, and so I'd wager that the correlation coeff would be about -0.5 or -0.6.

Answer 46

Glad to hear that this is starting to make more sense!

Answer 47

Okay, well it is 11 past midnight over here, so I am going to finish up this last question (which is just an opinionated question) and then I am going to go to sleep. Thank you for everything!

Answer 48

Opinion less than "educated guess". Great working with you; good night! bye.