35
Content
INTERPRETATI ON TECHNIQUE AND USE OF CORRELATION AND REGRESSION IN DATA ANALYSIS
By: Ruchika Chauhan BBM 3rd Year
2
MEANING OF INTERPRETATION
Interpretation means to bring out the meaning of data or we can say that interpretation is to convert data into information.
Interpretation
refers to the task of drawing inferences
from the collected facts after an analytical and/or experimental study. In fact, it is a search for broader meaning of research findings.
3
TWO ASPECTS OF INTERPRETATION
(i)
The effort to establish continuity in research through linking the results of a given study with those of another.
(ii) Interpretation
is the device through which the factors that
seem to explain what has been observed by researcher in the course of the study can be better understood and it also provides a theoretical conception which can serve as a
guide for further researches.
4
WHY INTERPRETATION?
It is being considered a basic component of research process because of the following reasons:
Through
Interpretation the researcher can well understand
the abstract principle that works beneath his findings.
Researcher
can
better
appreciate
only
through
interpretation why his findings are what they are and can make others to understand the real significance of his research findings.
5
Interpretation
is involved in the transition from
exploratory to experimental research.
Interpretation leads to the establishment of explanatory concepts that can serve as a guide for future research
studies.
6
TECHNIQUE
Technique of Interpretation involves following steps:
Researcher
must give reasonable explanations of the
relations which he has found and must try to find out the thread of uniformity that lies under the surface layer
of his diversified research findings.
Extraneous
Information if collected during the study,
must be considered while interpretation the final results
of research study.
7
Before
embarking upon final Interpretation, consult
someone having insight into the study and who is frank and honest and will not hesitate to point out the omissions and errors in logical argumentation.
Researcher
must accomplish the task of interpretation,
only after considering all relevant factors affecting the problem to avoid false generalization.
8
PRECAUTIONS IN INTERPRETATION
Researcher must pay attention to the following points for correct Interpretation:
At
the outset, researcher must invariably satisfy himself that
(a) the data are appropriate, trustworthy and adequate for drawing inferences (b) the data reflect good homogeneity
(c) proper analysis has been done through statistical methods
9
The
researcher must remain cautious about the errors that
can possibly arise in the process of interpreting results.
Researcher
must always keep in view that the task of
Interpretation is very much intertwined with analysis and cannot be distinctly separated.
Broad
generalisation should be avoided as most
research is not amenable to it because the coverage may be restricted to a particular time, a particular area and particular conditions.
10
USE OF CORRELATION AND REGRESSION IN DATA ANALYSIS
11
CORRELATION
Correlation
is a measure of association between two
variables.
Provides
an answer to the question:
Does there exist association or correlation between the two (or more) variables? If yes, of what degree?
Measures
and describes the strength and direction of
the relationship.
12
Bivariate
techniques requires two variable scores from
the same individuals (dependent and independent variables)
Multivariate
when more than two independent variables
(e.g. effect of advertising and prices on sales)
The
two most popular correlation coefficients are:
Spearman's correlation coefficient “rho” and Pearson's
product-moment correlation coefficient.
13
SCATTER PLOTS AND
TYPES OF CORRELATION
14
60 50 40 Accidents 30 20 10 0 0 2 4 6 8 10 12 14 16 18 20
Hours of Training
Negative Correlation–as x increases, y decreases
15
4.00 3.75 3.50 3.25 3.00 2.75 2.50 2.25 2.00 1.75 1.50
GPA
16
17
18
19
Absences X
Final Grade Y
Final Grade
95 90 85 80 75 70 65 60 55 50 45
x 8 2 5 12 15 9 6
0 2 4 6 8 10 Absences X 12 14 16
y 78 92 90 58 43 74 81
20
21
REGRESSION
Regression
indicates the degree to which the variation in
one variable X, is related to or can be explained by the variation in another variable Y.
Once
it is know that there is a significant linear
correlation, we can write an equation describing the
relationship between the x and y variables. This equation is called the line of regression or least squares line.
22
The
equation of a line may be written as
y = mx + b
where m is the slope of the line and b is the y-intercept.
The
line of regression is: slope m is:
The
The
y-intercept is:
23
24
25
26
27
Strength of the Association
The coefficient of determination, r2, measures the strength of the association and is the ratio of explained variation in y to the total variation in y.
The correlation coefficient of number of times absent and final grade is r = –0.975. The coefficient of determination is r2 = (– 0.975)2 = 0.9506.
28
Interpretation: About
95% of the variation in final grades can be explained by the number of times a student is absent. The other 5% is unexplained and can be due to sampling error or other variables such as intelligence, amount of time studied, etc.
29
REFERENCES
•William H. Kruskal and Tanur. Judith M. ed. (1978), "Linear Hypotheses," International Encyclopedia of Statistics. Free Press, v. 1 •Williams. Evan J. "I. Regression," pp. 523–41. •Stanley. Julian C. "II. Analysis of Variance," pp. 541–554. •D.V. Lindley, (1987). "Regression and correlation analysis," New Palgrave: A Dictionary of Economics, v. 4, pp. 120–23. •Birkes.David and Dodge, Y., Alternative Methods of Regression. ISBN 0-471-56881-3 •Chatfield, C. (1993) "Calculating Interval Forecasts," Journal of Business and Economic Statistics, 11. pp. 121–135. •Draper, N.R.; Smith, H. (1998). Applied Regression Analysis (3rd ed.). John Wiley. ISBN 0-471-17082-8. •Fox, J. (1997). Applied Regression Analysis, Linear Models and Related Methods. Sage •Kothari.C.R, “Research Methodology Methods and Techniques”.
30
Websites www.slideshare.net www.scribd.com www.oogle.com
31
THANKYOU
By: Ruchika Chauhan BBM 3rd Year
2
MEANING OF INTERPRETATION
Interpretation means to bring out the meaning of data or we can say that interpretation is to convert data into information.
Interpretation
refers to the task of drawing inferences
from the collected facts after an analytical and/or experimental study. In fact, it is a search for broader meaning of research findings.
3
TWO ASPECTS OF INTERPRETATION
(i)
The effort to establish continuity in research through linking the results of a given study with those of another.
(ii) Interpretation
is the device through which the factors that
seem to explain what has been observed by researcher in the course of the study can be better understood and it also provides a theoretical conception which can serve as a
guide for further researches.
4
WHY INTERPRETATION?
It is being considered a basic component of research process because of the following reasons:
Through
Interpretation the researcher can well understand
the abstract principle that works beneath his findings.
Researcher
can
better
appreciate
only
through
interpretation why his findings are what they are and can make others to understand the real significance of his research findings.
5
Interpretation
is involved in the transition from
exploratory to experimental research.
Interpretation leads to the establishment of explanatory concepts that can serve as a guide for future research
studies.
6
TECHNIQUE
Technique of Interpretation involves following steps:
Researcher
must give reasonable explanations of the
relations which he has found and must try to find out the thread of uniformity that lies under the surface layer
of his diversified research findings.
Extraneous
Information if collected during the study,
must be considered while interpretation the final results
of research study.
7
Before
embarking upon final Interpretation, consult
someone having insight into the study and who is frank and honest and will not hesitate to point out the omissions and errors in logical argumentation.
Researcher
must accomplish the task of interpretation,
only after considering all relevant factors affecting the problem to avoid false generalization.
8
PRECAUTIONS IN INTERPRETATION
Researcher must pay attention to the following points for correct Interpretation:
At
the outset, researcher must invariably satisfy himself that
(a) the data are appropriate, trustworthy and adequate for drawing inferences (b) the data reflect good homogeneity
(c) proper analysis has been done through statistical methods
9
The
researcher must remain cautious about the errors that
can possibly arise in the process of interpreting results.
Researcher
must always keep in view that the task of
Interpretation is very much intertwined with analysis and cannot be distinctly separated.
Broad
generalisation should be avoided as most
research is not amenable to it because the coverage may be restricted to a particular time, a particular area and particular conditions.
10
USE OF CORRELATION AND REGRESSION IN DATA ANALYSIS
11
CORRELATION
Correlation
is a measure of association between two
variables.
Provides
an answer to the question:
Does there exist association or correlation between the two (or more) variables? If yes, of what degree?
Measures
and describes the strength and direction of
the relationship.
12
Bivariate
techniques requires two variable scores from
the same individuals (dependent and independent variables)
Multivariate
when more than two independent variables
(e.g. effect of advertising and prices on sales)
The
two most popular correlation coefficients are:
Spearman's correlation coefficient “rho” and Pearson's
product-moment correlation coefficient.
13
SCATTER PLOTS AND
TYPES OF CORRELATION
14
60 50 40 Accidents 30 20 10 0 0 2 4 6 8 10 12 14 16 18 20
Hours of Training
Negative Correlation–as x increases, y decreases
15
4.00 3.75 3.50 3.25 3.00 2.75 2.50 2.25 2.00 1.75 1.50
GPA
16
17
18
19
Absences X
Final Grade Y
Final Grade
95 90 85 80 75 70 65 60 55 50 45
x 8 2 5 12 15 9 6
0 2 4 6 8 10 Absences X 12 14 16
y 78 92 90 58 43 74 81
20
21
REGRESSION
Regression
indicates the degree to which the variation in
one variable X, is related to or can be explained by the variation in another variable Y.
Once
it is know that there is a significant linear
correlation, we can write an equation describing the
relationship between the x and y variables. This equation is called the line of regression or least squares line.
22
The
equation of a line may be written as
y = mx + b
where m is the slope of the line and b is the y-intercept.
The
line of regression is: slope m is:
The
The
y-intercept is:
23
24
25
26
27
Strength of the Association
The coefficient of determination, r2, measures the strength of the association and is the ratio of explained variation in y to the total variation in y.
The correlation coefficient of number of times absent and final grade is r = –0.975. The coefficient of determination is r2 = (– 0.975)2 = 0.9506.
28
Interpretation: About
95% of the variation in final grades can be explained by the number of times a student is absent. The other 5% is unexplained and can be due to sampling error or other variables such as intelligence, amount of time studied, etc.
29
REFERENCES
•William H. Kruskal and Tanur. Judith M. ed. (1978), "Linear Hypotheses," International Encyclopedia of Statistics. Free Press, v. 1 •Williams. Evan J. "I. Regression," pp. 523–41. •Stanley. Julian C. "II. Analysis of Variance," pp. 541–554. •D.V. Lindley, (1987). "Regression and correlation analysis," New Palgrave: A Dictionary of Economics, v. 4, pp. 120–23. •Birkes.David and Dodge, Y., Alternative Methods of Regression. ISBN 0-471-56881-3 •Chatfield, C. (1993) "Calculating Interval Forecasts," Journal of Business and Economic Statistics, 11. pp. 121–135. •Draper, N.R.; Smith, H. (1998). Applied Regression Analysis (3rd ed.). John Wiley. ISBN 0-471-17082-8. •Fox, J. (1997). Applied Regression Analysis, Linear Models and Related Methods. Sage •Kothari.C.R, “Research Methodology Methods and Techniques”.
30
Websites www.slideshare.net www.scribd.com www.oogle.com
31
THANKYOU
