Introduction to the literature in the field of thermoelectricityDescripción completa
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MCQs on Correlation and Regression Analysis with Answers by http://itfeature.com
Draper, N., Smith, H. (1998), Applied Regression Analysis, John Wiley, New York.Descripción completa
Unit – II (Regression Analysis) Q. Write a short note on Regression analysis. Ans: Regression analysis is a statistical tool with the help of which it is possible to predict the value of one variable (dependent variable) using the value of known variable (independent variable). Dependent variable is called regressed variable or explained variable and denoted by Y whereas independent variable is called regresser or predictor or explanatory variable. Utility of regression analysis 1. It helps in the formulation and determination of functional relationship between two or more variables. 2. It helps in establishing a cause and effect relationship between two variables in economics and business research. 3. It helps in predicting and estimating the value of dependent variable as price, production, sales etc. 4. It helps to measure the variability or spread of values of a dependent variable with respect to the regression line. Q. Write the difference between correlation and regression. Correlation Regression 1. It studies the degree of relationship 1. It studies the nature of relationship between variables. between variables. 2. It need not imply cause and effect 2. It implies cause and effect relationship relationship between variables. between variables. 3. There may be nonsense correlation 3. There is nothing like nonsense between the variables. regression. 4. The correlation coefficient is 4. The regression coefficients are only independent of change of scale and independent of change of origin but not origin. of scale. 5. The correlation coefficient cannot be 5. The regression lines can be used for used for prediction. prediction. Q: Write a note on regression lines. Ans: For two variables X and Y, there will be two regression lines. The regression line of X on Y and regression line of Y on X. The regression line of X on Y estimates the values of X for the given values of Y. Similarly, the regression line of Y on X estimates the values of Y for given values of X. When there is perfect positive or negative correlation between two variables, the regression lines coincides. Thus, closer are the regression lines, the smaller the angle between them and greater is the degree of correlation between them. If two variables are uncorrelated or independent, the regression lines will be perpendicular to each other. The two regression lines ̅ ̅. intersect each other at ( Regression equations: Regression equations are mathematical expression of regression lines. The regression equation of Y on X is expressed as Y = a + bX , where a and b are two constants. The constant a indicates the intercept and b is called the regression coefficient of Y on X and is written as bYX(b1). Similarly, the regression equation of X on Y is expressed as X = a + bY . Here b is called the regression coefficient of X on Y and is written as b XY(b2). bYX(b1) shows the
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change in the value of Y with a unit change in the value of X and b XY(b2) shows the change in the value of X with a unit change in the value of Y. Properties of Regression coefficient 1. Correlation coefficient is the geometric mean between two regression coefficients. i.e.
√ . 2. Both regression coefficients must have the same sign. 3. The correlation coefficient will have the same sign as that of the two regression coefficients. 4. If one of the regression coefficients is greater than unity, the other must be less than unity, because coefficient of correlation cannot be more than unity. 5. The arithmetic mean of regression coefficients b XY and bYX is greater than or equal to the correlation coefficient r i.e. ½ (bXY + bYX) ≥ r. 6. Regression coefficients are independent of origin but not of scale. Important Points 1. The two regression equations are not reversible. 2. The two regression lines are different except when r = 1. In such case the lines become identical. When r = 0 then the variables are uncorrelated and no line can be estimated using the other line. 3. If it is not known which equation behaves as regression line of Y on X and which as regression line of X on Y, then calculate r using the assumptions made, if r < 1 then the assumptions are correct otherwise reverse the assumptions.
