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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.
Differentiate numeral coefficient from literal coefficient?
numeral coefficient or numerical coefficient is a number used in an algebraic term, while literal coefficient is the letter used to represent a number.
Properties of regression coefficient-statistics?
8.7.4 Properties of Regression Coefficients:(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, providedr > 0.(d) Regression coefficients are independent of the changes of origin but not of scale.
What is regression coefficient and correlation coefficient?
The strength of the linear relationship between the two variables in the regression equation is the correlation coefficient, r, and is always a value between -1 and 1, inclusive. The regression coefficient is the slope of the line of the regression equation.
What are the properties of correlation coefficient?
The correlation coefficient is symmetrical with respect to X and Y i.e.The correlation coefficient is the geometric mean of the two regression coefficients. or .The correlation coefficient lies between -1 and 1. i.e. .
What are the properties of correlation?
The correlation coefficient is symmetrical with respect to X and Y i.e.The correlation coefficient is the geometric mean of the two regression coefficients. or .The correlation coefficient lies between -1 and 1. i.e. .
What is numerical range of regression coefficient?
ɪf the regresion coefficient is the coefficient of determination, then it's range is between 0 or 1. ɪf the regression coefficient is the correaltion coefficient (which i think it is) the it must lie between -1 or 1.
Can regression be meassurd?
Regression can be measured by its coefficients ie regression coefficient y on x and x on y.
What is the relationship between correlation coefficient and linear regreassion?
A correlation coefficient is a value between -1 and 1 that shows how close of a good fit the regression line is. For example a regular line has a correlation coefficient of 1. A regression is a best fit and therefore has a correlation coefficient close to one. the closer to one the more accurate the line is to a non regression line.
What does the coefficient of determination explain in regression?
The coefficient, also commonly known as R-square, is used as a guideline to measure the accuracy of the model.
What is a measure of the explanatory power of the regression model?
Regression analysis describes the relationship between two or more variables. The measure of the explanatory power of the regression model is R2 (i.e. coefficient of determination).
What is the r in mathematics?
The answer depends on the context. In geometry it is usually the radius, in statistics it is the regression coefficient.
When all of the points fall on the regression line what is the value of the correlation coefficient?
1 or -1
What is the sign of slope of the regression line if the correlation coefficient is -0.15?
The sign is negative.
