Page 236 - DMGT209_QUANTITATIVE_TECHNIQUES_II

Unit 11: Multiple Regression and Correlation Analysis

 The general form of the line of regression of Y on X is YCi = a + bXi, where YCi denotes the Notes
average or predicted or calculated value of Y for a given value of X = Xi.
 Multiple regressions are a statistical technique that allows us to predict someone’s score
on one variable on the basis of their scores on several other variables. An example might
help.

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 There are several different definitions of R which are only sometimes equivalent. One
class of such cases includes that of linear regression.
 The least-squares regression line is the line that makes the sum of the squares of the
vertical distances of the data points from the line as small as possible.
 Non-parametric regression analysis traces the dependence of a response variable on one
or several predictors without specifying in advance the function that relates the response
to the predictors.

11.6 Keywords

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Coefficient of determination: In statistics, the coefficient of determination R is used in the context
of statistical models whose main purpose is the prediction of future outcomes on the basis of
other related information.

Regression Equation: If the coefficient of correlation calculated for bivariate data (Xi, Yi), i = 1, 2,
...... n, is reasonably high and a cause and effect type of relation is also believed to be existing
between them, the next logical step is to obtain a functional relation between these variables.
This functional relation is known as regression equation in statistics.

11.7 Review Questions

1. Distinguish between correlation and regression. Discuss least square method of fitting
regression.
2. What do you understand by linear regression? Why there are two lines of regression?
Under what condition(s) can there be only one line?
3. What do you think as the reason behind the two lines of regression being different?
4. For a bivariate data, which variable can we have as independent? Why?
5. What can you conclude on the basis of the fact that the correlation between body weight
and annual income were high and positive?

Answers: Self Assessment

1. ei
2. Line of regression
3. Logistic regression

4. Coefficient of determination

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