BASIC STATISTICS RELATED QUESTION - Regression and Correlation

ALPHA and BETA are two physical quantities:

A is dependent variable (Y-Axis) and B is independent variable (X-Axis).

Values of ALPHA range from 50 to 250. (with steps of 50 i.e. 50, 100, 150, 200, 250 )

Values of BETA range from -2 to 3. (with steps of 1 i.e. -2, -1, 0, 1, 2, 3)

Following points are to be plotted on the graph made by ALPHA and BETA.

R(-0.9,175)

K(-0.9,170)

E(-0.5,140)

D(-0.7,110)

N(-0.3,120)

Q(0,145)

S(0.1,80)

G(0.1,60)

H(0.2,150)

T(0.40,120)

A(0.5,80)

P(0.9,125)

Y(1.25,190)

M(1.45,165)

V(1.35,140)

C(1.80,110)

L(1.9,170)

I(1.95,170)

F(1.95,180)

W(2.5,235)

PLOT these points on ALPHA vs BETA GRAPH.

For which subset of characters(above mentioned points), there is fairly linear relationship and for which subset of characters does it deviate the most ? Is there any need to find errors also ? How would we assure whatever answer we have got is correct ? (Any verification method?)

I know it is very simple statistics problem. PLEASE REPLY SOON. Since I am a beginner in Statistics, I don't know how to solve this problem.

Answer 1

[Matthias]

Use the curve fitting toolbox to make a linear fit with all your points and throw out all which are further away than the standart distribution. Usually the throwing out of points is done by the fitting tool to(if you want to).

[Priya]

Since I am a beginner in Statistics, I just want to know the logic behind answering this question. Then I will find matlab functions to do this.

Answer 2

[Image Analyst]

In general, it's not quite such a simple process. For example, look at the scatterplot of points on this page of Wikipedia for RANSAC: http://en.wikipedia.org/wiki/Ransac. To find only the points that are along the line is not necessarily trivial. This is the reason why the RANSAC method was developed. I'm not sure if there are RANSAC programs in the File Exchange, but you might look, otherwise program up the pseudocode from Wikiepdia.

[Priya]

Since I am a beginner in Statistics, I just want to know the logic behind answering this question. Then I will find matlab functions to do this.

[Image Analyst]

I don't know if they were expecting you to use RANSAC or not, but that's how I'd do it. It's possible that they covered some other way in your class and then that's what you should use. The Wikipedia article does give the reasoning (logic) for why it works.