Help with Different Types of Regression

[Iamadam]

Hello.

I have the data:

--------------------------------------------
|Distance (feet) | Shooting Percentage 
|-------------------------------------------
  3               |         62
  6               |         52
  9               |         40
 12               |         32
 15               |         28
 18               |         24
 21               |         21
 24               |         20
 27               |         18
 30               |         17
 40               |         13
-------------------------------------------

Now I have a few questions which I am unsure about.

Firstly, why does this represent a continuous function? I never completely grasped the whole continuous\discreet thing. I know that continuous data is non whole number....but yeah It's not very clear to me why this is continuous.

Secondly, what type of regression could be used to model this data? I really have no idea. I'm pretty sure linear regression would be inaccurate. I tried the other types on my calculator (x^2, x^3, x^4 and logarithmic) and thought they all modeled the data well. The problem is, the very next question asks : why would it be inapproapriate to model this data using a power resression or a sinusoidal regression?
So now I'm completely stumped. I don't even know fully what logarithmic and simusoidal regression is!

Please, please will someone help me here. If you don't have time to help with both, help with the second part please
I'm so stressed about this.
Thanks in advance
-Adam

 

[stapel]

Firstly, why does this represent a continuous function?

Hint: Look at what is being measured.

Secondly, what type of regression could be used to model this data?

Hint: Plot the data. What sort of curve does it look like?

I don't even know fully what logarithmic and simusoidal regression is!

They are regressions which use logarithms or sines for their modelling functions.

Eliz.

 

[Iamadam]

Thankyou for your help with this.
I have plotted the datam but still do not understand why a power regression would not be a good way to mdel the data.
Any further help would be appreciated
-Adam

 

[mcrae]

linear would be bad because in theory at a distance of 0 metres shooting % should be 100%, and at a distance beyond 43 metres the LOBF says shooting % will by below 0, which isnt true.

power regression says that at 1000m your shootign % is still 1.9%, which i doubt is true at all

 

[Iamadam]

Thankyou very much! I never even though of checking that.
I am still unsure on periodic regression, but this has helped immensely! Thankyou!

I know that periodic (sinusoidal) data makes a 'wavy' graph, but I don't understand the significance of this in relation to the question.

Further help would be appreciated, but what you have given so far has helped alot!
Thankyou again
-Adam

 

[Gene]

As Staple hinted, there is nothing to keep you from shooting at 3.0001 feet nor from getting 61.9%. That is why it is continuous. With something like dice you can't roll 3.1 times and can't roll a 4.5 which makes it discrete.
I can think of no way that you would go down from 3' to 4' then up from 4' to 5', down from 5' to 6'... That would be necessary for a perodic model.
I'm not sure mcrae's argument against linear is valid. As long as it models the data in the domain I think it cannot be dismissed but from a logical approach if the gun sight wavers the same number of degrees, at twice the distance I would expect the percent to go down by a square factor, because of the effect of the area it would be covering while the bullseye area stays the same.
Just some thoughts.
-----------------
Gene

 

[Iamadam]

Thankyou for the help everyone, I really appreciate it.