The document discusses various concepts related to time series analysis and correlation. It defines time series as a sequence of data points measured over successive time periods. Time series analysis is used to extract meaningful patterns from temporal data and forecast future values. Correlation analysis examines the relationship between two quantitative variables, and can be positive, negative, linear or non-linear. Regression analysis is used to estimate the value of a dependent variable based on the value of an independent variable. Key components of time series include trends, cyclical variations, seasonal variations, and irregular variations.

2. CORRELATION
• A Statistical technique that is used to analyse the
strength and direction of the relationship between
two quantitative variable is called Correlational
analysis.
• Two variables are said to be in correlation if the
change in one of the variable results in a change in
other variable.
E g :- 1) Frequency of smoking and lungs damage ,
2) Sales revenue and expenses incurred on
advertising.

3. Importance of correlation
• If variables are linearly related to each other
then it helps in estimation of one from the other.
– Advertisement and sales
– Prices and Demand
• We use Regression Analysis to find the value of
one variable from the other

4. TYPES OF CORRELATION
• POSITIVE AND NEGATIVE
• LINEAR AND NON-LINEAR
• SIMPLE ,PARTIAL AND MULTIPLE

5. POSITIVE CORRELATION AND
NEGATIVE CORRELATION
POSITIVE CORRELATION NEGATIVE CORRELATION
• If the variables vary in
same direction,
correlation is said to be
POSITIVE.
– If one variable increases,
the other also increases
on the other hand, if one
variable decreases, the
other also decreases.
• If both variables vary in
the opposite direction,
correlation is said to be
NEGATIVE.
– If one variable increases
and the other decreases,
or one decreases the
other increases.

6. LINEAR CORRELATION NON-
LINEAR CORRELATION
LINEAR CORRELATION
• If the extent of change in
one variable tends to
have a constant ratio in
the extent of change in
another variable, then the
correlation is said to be
LINEAR.
NON-LINEAR CORRELATION
• If the extent of change in
one variable tends to
have no consistent ratio
in the extent of change in
another variable, then the
correlation is said to be
NON-LINEAR.

7. SIMPLE,PARTIAL AND MULTIPLE
CORRELATION
• When only two variables are involved, it is
simple correlation
• When three or more than three variables
are involved, we can compute either
partial or multiple correlation

8. Methods of
correlation
graphic
Scatter diagram
algebraic
1. Karl pearson
2. Rank method

9. Scatter Diagram
Scatter diagram is a graph or chart which helps to
determine whether there is a relationship between two
variables by examining the graph of the observed data.
A scattered diagram can give us two types of information:
• Pattern that indicate that the variables are related.
• If the variables are related,what kind of line or
estimating equation,describes this relationship.

11. KARL’S PEARSONS
COEFFIENT OF CORRELATION
• Karl Pearson’s Coefficient of Correlation
denoted by- ‘r’ The coefficient of
correlation ‘r’ measure the degree of linear
relationship between two variables say x
& y.
r = N Σdxdy - Σdx Σdy
√N Σdx²-(Σdx)²√N Σdy²-(Σdy)²

12. The value of correlation coefficient ‘r’ ranges
from -1 to +1
If r = +1, then the correlation between the two
variables is said to be perfect and positive
If r = -1, then the correlation between the two
variables is said to be perfect and negative
If r = 0, then there exists no correlation
between the variables
Interpretation of Correlation
Coefficient (r)

13. REGRESSION
• The statistical technique that express the
relationship between two or more variables in the
form of an equation to estimate the value of a
variable, based on the given value of another
variable is called regression analysis.
eg :- Profit after Sales of a firm.

14. Difference between dependent variable
and independent variable
Independent Variable
1. The known variable is called
the independent variable.
2. What we typically call “X”.
3. Variable that is controlled or
manipulated.
4. It is plotted on horizontal axis.
5. An input variable.
Dependent Variable
1. The variable we are trying to
predict is the dependent
variable.
2. What we typically call ”Y”.
3. Variable that cannot be
controlled or manipulated.
4. It is plotted on vertical axis.
5. An output variable.

15. Difference between Regression
and Correlation
Regression
• A statistical method used
to describe the nature of
relationship.
• In linear regression analysis
one variable is considered
as dependent variable and
other as independent
variable
Correlation
• A statistical method used
to determine whether a
relationship between two
or more variables exist.
• In correlation analysis we
examine the degree of
association between two
variables

16. Advantages of Regression Analysis
• It helps in developing a regression equation
by which the value of a dependent variable
can be estimated given a value of an
independent variable.
• It helps to determine standard error of
estimate to measure the variability or spread
of values of a dependent variable with
respect to the regression line.

17. Estimation using the Regression Line
• The equation for a straight line where the
dependent variable Y is determined by the
independent variable X is:
Y = a + bx
Where,
a = y-intercept
b = slope of the line
Y = value of dependent variable
X = value of independent variable

18. THE METHOD OF LEAST SQUARE
• It is a method of having a “good fit” of a line
which minimizes the error between the
estimated points on the line and actual
points that were used to draw it.
• In this method Y represents the individual
value of the observed points measured along
the Y-axis and Y(y-hat) symbolize the
individual values of the estimated points.
• The Estimated Line is:
= a + bx

19. b = ∑XY -
∑X2
–n 2
a = -b
Where,
a = Y-intercept
b = slope of the best-fitting estimating line.
X = value of independent variable
Y = value of dependent variable
= mean of the values of the independent variable
= mean of the values of the dependent variable
x
x
y
xn y
y x

20. COEFFICIENT OF
DETERMINATION
• The convenient way of interpreting the value
of correlation coefficient is to use of square of
coefficient of correlation which is called
Coefficient of Determination.
• The Coefficient of Determination is r2.
r2
= 1- ∑(Y- )2
∑(Y-Y̅ )2

21. STANDARD ERROR OF ESTIMATE
Standard error of estimate measures the
variability of the scatter of the observed
values around the regression line.
It is given by:
Se= ∑(Y- )2
n-2
If Se=0, the estimating equation is expected to
be a “perfect” estimator of the dependent
variable.

22. WHAT DOES TIME-SERIES MEAN?
• A time series is a sequence of data points,
measured typically at successive points in time
spaced at uniform time intervals.
• Time series is a set of measurements of a
variable that are ordered through time
• Time series analysis comprises methods for
analyzing time series data in order to extract
meaningful statistics and other characteristics
of the data

23. DIFFERENCE WITH REGRESSION
ANALYSIS
• Time –series Analysis • Regression Analysis
Time series forecasting is the
use of a model to predict
future values based on
previously observed values.
Regression analysis is often
employed in such a way as
to test theories that the
current value of one time
series affects the current
value of another time
series.
Regression analysis cannot
explain seasonal and cyclical
effects.
It shows or suggests
periodicity of a data like
seasonal and cyclical
effects.

24. COMPONENTS OF TIME SERIES
• SECULAR TREND
• CYCLICAL VARIATIONS
• SEASONAL VARIATIONS
• IRREGULAR VARIATIONS

25. SECULAR TREND
A time-series which displays a steady tendency of
either upward or downward movement in the average
(or mean) value of the forecast variable (let us say ‘y’)
over a long period of time is called “Trend”.
If we talk about commodities, Secular Trend is affected by
prices, productions and sales of the commodity as well as the
population of the area.
Examples-
1. We find that over the last few years the sales of Laptop in
Ranchi has increased. so, we can say that the sales of Laptop
is showing an “ Upward Trend”.
2. Use of Landline Phone has decreased over the last few years.
This shows the “Declining Trend” of using Landline Phone.

26. Units
years
Upward trend of sales of Laptops in Ranchi
2000 2001 2002 2003 2004 2005 2006 2007
2000
4000
6000
8000
10000

27. units(in‘000)
years
Declining trend of using Landline Phones in India
2000 01 02 03 05 06 07 08 09 10 11
30
60
90
120
150
180
04

28. CYCLICAL VARIATION
Cyclical variations are long-term movements that represent
consistently recurring rises and declines in activity.
Timing is the most important factor which affect
the Cyclical Variations.
for example- Business Cycle, it consists of the recurrence of
the up and down movements of business activity

29. depression
prosperity
Prosperity or boom
Economicactivities
time
Cyclical Variation(Business cycle)

30. SEASONAL VARIATION
Seasonal variations are those periodic movements in business
activity which occur regularly every year.
Since these variations repeat during a period of twelve months
so, they can be predicted fairly accurately.
Seasonal Variations are caused by climate and weather
conditions, customs, festivals and habits.
for example-Sales of Cold-drinks goes up in summer season
than any other season

31. Units
years2000 2001 2002 2003 2004 2005 2006
Sales of Cold-drinks
10000
12000
14000
16000
18000
20000

32. IRREGULAR VARIATION
Irregular variations refer to such variations in business
activity which do not repeat in a definite pattern.
In these type of variations the pattern of the variable is
unpredictable.
Irregular Variations are caused by unpredictable
factors like natural disasters (earthquakes, floods,
wars etc.).These are unpredictable and no one
has control over it.
For example-Production of cars tremendously went
down after earthquake came in Japan in Nov 2011.

33. 2005 2006 2007 2008 2009 2010 2011
100000
150000
200000
250000
300000
350000
units
Production of cars in Japan
years

34. NEED OF TIME-SERIES ANALYSIS
Helpful in evaluating current accomplishments
Actual performances can be compared with
the expected performance and the cause of the
variations analysed
Facilitates comparison.
Different time-series can be compared
and important conclusions can be drawn from
this with the help of this we can take decisions

35. Thank you…