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(a) Correlation coefficient is the geometric mean between the regression coefficients.
(b) If one of the regression coefficients is greater than unity, the other must be less than unity.
(c) Arithmetic mean of the regression coefficients is greater than the correlation coefficient r, provided
r > 0.
(d) Regression coefficients are independent of the changes of origin but not of scale.
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When doing linear regression if the correlation coefficient is positive the slope of the line is negative?
False.
What is the physical significance of damping coefficient?
The damping coefficient applies both to hydraulic circuits and springs. Hydraulics In general, higher the coefficient or viscosity higher is the tendency to ensure steady flow and hence a higher system efficiency. This is governed by the properties of hydraulic oil selected for use. Springs Higher the coefficient, greater is the tendency for a spring to reach a desired equilibrium position. This is governed by the properties of spring material selected for the applciation.
When coefficient of correlation is not perfect you should use an appropriate regression line for projection?
When the correlation coefficient isn't equal to 1 you have any number of choices. Contrary to what a maths syllabus might tell you, there is no right or wrong answer here. Do whatever you think best! Maths does have a creative element to it (this isn't it though...) If its close to zero though, a regression line is probably a poor choice. There aren't many ways to draw a nice fitting curve in this case, but you might be able to model it with a random (e.g. bivariate normal) distribution.
What is used to show the relationship between two factors?
Ideally a mapping, or a scatter plot. Not a function because it should not map one value to many (eg square root). Not the regression coefficient since for an even function it would be 0.
Relationship between coefficient lift and coefficient drag?
For cylinders coefficient of lift is approximately half of coefficient of drag while they are equal for Aerofoils.
