Regression equation?

Question

State the type of mathematical relationship that exists. Once you've recognized the type of relationship (linear, quadratic, or exponential determine the regression equation for this relationship? Explain your reasoning for this type of relationship? x= 1,3,5,7,9,11,13,15

y= 50,14,2,14,50,50,194,302

 

Using my TI - 83 calculator i got the following answers...

y=ax+b
a=16.9285294
b=-50.92857143
r^2=.6047285294
r=.7776429318
y=16.92857143x+-50.92857143

Linear
---------------------------------
y=ax^2+b+c

a=3.367857143
b=-35.35714286
c=89.58928571
r^2=.9652788993
Quad

-----------------------------------
y=a*b^x
a=6.29733766
b=1.243871537
r^2=.4489101455
r=.6700075712
Exp

 

 

 

How do i know which one is right??

Answer 1

The first step is to determine the kind of relationship, not to run the regression.

 

One way to do this is to graph the points and see if you can see a familiar shape to the data points.  In this case, you have to scale the y-axis because the range of y-values is very large.  But that's easy to do.  When you graph these points it's pretty easy to see that it looks like a quadratic, with one outlier.  The y value for x=11 seems to be out of place, but that can happen in the real world.