0

Are 5 observations enough to verify the following non-linear regression model in the form: $ Y= C K_0^{\alpha_0}K_1^{\alpha_1}K_2^{\alpha_2}$ And in general how many observations do I need for models of this kind?

chen h.
  • 723
  • Are you trying to fit six parameters from five observations? Or are some of the terms in the right hand side of $Y$ knowns? – hardmath Aug 18 '14 at 12:29
  • C,$\alpha_0,\alpha_1,\alpha_2$ are known constants. I have observations for $K_0, K_1$ and $ K_2$ in five years 1990-1994. My hypothesis is that the regression model has this form. But my professor told me that I cant test regression hypothesis with so few observations and I got F!!! – chen h. Aug 18 '14 at 12:35
  • These are important elements of your Questions. You should edit the Question to include the specification of $K_0,K_1,K_2$ as unknowns (with other terms given). – hardmath Aug 18 '14 at 12:38

1 Answers1

0

Are all of those variables unknown? If so, then $5$ won't cut it. Take the logarithm of both sides and convert the problem into a linear regression problem. To solve the resulting set of linear equations, you will need at least $7$ data points.

I just realized: where is your independent variable, $X$?

Calculon
  • 5,725
  • The independent variable s K. I have three independent variables. It's multiple regression. My professor told me that I cant run regression analysis with less than 30 observations. Is this true? – chen h. Aug 18 '14 at 11:46
  • Then, you need $4$ data points. The reasoning in my answer still applies. – Calculon Aug 18 '14 at 11:49
  • Thank you. But why my professor told me that I should never use regression analysis with less than 30 observations? Is he wrong?? – chen h. Aug 18 '14 at 11:50
  • Well, professors, just like anybody else, can be wrong. It really depends on the model you are trying to fit. $4$ in my comment is a bare minimum to get a solution for your parameters. But that is likely to result in overfitting. So it would be wise to have more than $4$ data points. – Calculon Aug 18 '14 at 11:55
  • Thanks.But If I understand correctly in order to test the significance of the independent variables and use the limit theorems, I must have a lot more observations, am I right? I am new to this field and I don't know whether my question makes sense. I have 5 observations for 5 independent variables but I think that the other two are not important for the model so I excluded them. My hypothesis is that the regression has the form above. It's a hypothesis, I don't know whether this is true. – chen h. Aug 18 '14 at 12:01
  • @chenh.: It should be clear to you now that you are dribbling out pieces of information crucial to answering the query, how many observations are needed. Please edit the Question, and don't forget to explain the role of independent variable(s) in your observations. – hardmath Aug 18 '14 at 12:40