Page 204 - DMGT404 RESEARCH_METHODOLOGY

Research Methodology

Notes  Straight-line (linear) relationships are particularly important because a straight line is a
simple pattern that is quite common.
 The correlation measures the direction and strength of the linear relationship.
 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.

9.6 Keywords

Correlation: It is an analysis of covariation between two or more variables.
Correlation Coefficient: It is a numerical measure of the degree of association between two or
more variables.

Kernel Estimation: The kernel regression is a non-parametric technique in statistics to estimate
the conditional expectation of a random variable.
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.
Smoothing Splines: It is a method of fitting a smooth curve to a set of noisy observations using
a spline function.
9.7 Review Questions

1. Obtain the two lines of regression from the following data and estimate the blood pressure
when age is 50 years. Can we also estimate the blood pressure of a person aged 20 years on
the basis of this regression equation? Discuss.

Age (X) (in years) 56 42 72 39 63 47 52 49 40 42 68 60
Blood Pressure (Y) 127 112 140 118 129 116 130 125 115 120 135 133

2. Show that the coefficient of correlation, r, is independent of change of origin and scale.
3. Prove that the coefficient of correlation lies between – 1 and + 1.
4. “If two variables are independent the correlation between them is zero, but the converse
is not always true”. Explain the meaning of this statement.
5. What is Spearman’s rank correlation? What are the advantages of the coefficient of rank
correlation over Karl Pearson’s coefficient of correlation?
6. Distinguish between correlation and regression. Discuss least square method of fitting
regression.
7. What do you understand by linear regression? Why there are two lines of regression?
Under what condition(s) can there be only one line?
8. What do you think as the reason behind the two lines of regression being different?

9. For a bivariate data, which variable can we have as independent? Why?
10. What can you conclude on the basis of the fact that the correlation between body weight
and annual income were high and positive?

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