A Business Encyclopedia

Properties of Regression Coefficient

Definition: The constant ‘b’ in the regression equation (Ye = a + bX) is called as the Regression Coefficient. It determines the slope of the line, i.e. the change in the value of Y corresponding to the unit change in X and therefore, it is also called as a “Slope Coefficient.”

Properties of Regression Coefficient

  1. The correlation coefficient is the geometric mean of two regression coefficients. Symbolically, it can be expressed as:roperties of Regression Coefficient-1
  2. The value of the coefficient of correlation cannot exceed unity i.e. 1. Therefore, if one of the regression coefficients is greater than unity, the other must be less than unity.
  3. The sign of both the regression coefficients will be same, i.e. they will be either positive or negative. Thus, it is not possible that one regression coefficient is negative while the other is positive.
  4. The coefficient of correlation will have the same sign as that of the regression coefficients, such as if the regression coefficients have a positive sign, then “r” will be positive and vice-versa.
  5. The average value of the two regression coefficients will be greater than the value of the correlation. Symbolically, it can be represented asRegression Coefficient-2
  6. The regression coefficients are independent of the change of origin, but not of the scale. By origin, we mean that there will be no effect on the regression coefficients if any constant is subtracted from the value of X and Y. By scale, we mean that if the value of X and Y is either multiplied or divided by some constant, then the regression coefficients will also change.

Thus, all these properties should be kept in mind while solving for the regression coefficients.


Leave a Reply

Your email address will not be published. Required fields are marked *


Related pages

accelerators definitionmeaning of marketersindefference curveteleological theories focus onbureaucracy theory definitionequation of budget linemotives of inventory managementscatter diagram definitioncommercial paper secondary marketsix sigma methodologiesrupee depreciation meaningdiversification economics definitioncorporate jargonsfrontal attack strategy exampledifference between primal and dual problemwhat does debenture mean in financewhat is trait theory of personalitysenior citizen deposit scheme post officeagree disagree likert scaledescribe neoclassicismprovident fund act in indiastructural unemploymenttraining process in hrmcognitive conditioning definitionwhat is poaching meanyohari windowhenri fayolexpectancy theory psychologymeaning ipomarketing channel conflict examplesadvantages and disadvantages of job evaluationunsolicited definejahari windowdefinition of proprietorshippoacher meaningdefine autocratshybrids meaningdisguises definitionwhat is deontological ethical theorysources of secondary data in marketing researchmarginal cost in cost accountingblake and mouton management gridarbitrage definitionexplain the difference between accounting profit and economic profitdefination of oligopolyrepo rate definition rbikisan vikas patra for nrifree rein leadership definitionwhy indifference curve is convex to the originwalter dividend modelbalanced scorecard dimensionspolycentric attitudeabout henri fayoladvantages and disadvantages of m commercecardial meaningcross elasticity of demand for complementary goodsrepo rate defineliability clause in memorandum of associationexamples of superegodifference between brand equity and brand imagemeaning of hostile takeoverdeterminant of price elasticityaccelerator economics definitionsystematic sampling in statisticsfixed installment methodstuctural unemploymentconciliation officer meaningreturn on capital employed ratio formulawhat does loafing meanlaissez faire translationmeaning of neft in banking termsdonkey carrot stickdefinition of equipmentsgreenmail paymentvroom s expectancy theory