1. What is Correlation Analysis?
Correlation Analysis measures the degree of linear association between two or more variables.
If a change in one variable results in a corresponding change in the other variable either in the same direction or in the opposite direction, we say the variables are correlated.
The popular methods to assess Correlation are Scatter Diagram & Karl Pearson’s Correlation Coefficient

2. Karl Pearson’s Correlation Coefficient
The value of ‘r’ lies between -1 & +1

3. Using Regression Analysis in Forecasting
Regression Analysis is a statistical technique that can be used to develop a mathematical equation between two or more variables. In regression, the variable that is being predicted is called dependent variables and the variables used to predict the value of the dependent variable are called independent or explanatory variables.
Regression analysis involving one independent variable and one dependent variable with a straight line relationship is called simple linear regression. Regression analysis involving two or more explanatory variables is called multiple regression analysis.

4. What is Regression Analysis?
Regression Analysis is the study of the dependence of one variable (dependent variable) on one or more other variable (explanatory variable) in order to determine the average value of the dependent variable given the values of the explanatory variable.
Based on the past data, we calculate the regression model (coefficients) & then using the regression model we estimate the average value of the dependent variable for given or known value of the independent variable

5. Regression Analysis
The regression equation of Y on X is expressed as follows:
Where
is the estimate of the dependant variable Y
is the regression coefficient (Intercept term)
is the regression coefficient (Slope of the line)
is the explanatory variable

6. Regression Analysis

7. Regression Analysis The following are the formulas for the estimators;
Where
The Coefficient of Determination = r2
(0  r2  1)

8. Using Trend Projection in Forecasting
When we use regression analysis to relate the variable that we want to forecast to other variables that are supposed to influence that variable, it becomes a causal forecasting method. Using regression analysis for trend projection is not a causal forecasting method because only past values of sales, the variable being forecast, are used.
If we use simple linear regression to fit to a linear trend to sales time series then, the sales isn’t actually causally related to time, instead time is a surrogate for variables to which sales is actually related, but which are unknown or too difficult or costly to measure.

9. Using Trend Projection in Forecasting
The type of time series pattern for which the trend projection method is applicable shows a consistent increase or decrease over time. It is not stable. So the smoothing methods are not applicable.
The trend component does not follow each and every up and down movement. Rather the trend component reflects the gradual shifting, for example, growth of time series values.

10. Trend Analysis in Time Series

11. Using Regression for Trend Analysis
is the estimated Sales value
is the intercept term
is the slope of the regression line
is the time variable (surrogate variable)

12. Using Trend and Seasonal Components in Forecasting
Many situations in business & economics involve period to period comparisons for example use of electricity consumption is down 3% from the previous month. Care must be exercised in using such information because whenever a seasonal influence is present, such comparisons usually are not meaningful. For example the use of electricity consumption is down 3% might be a seasonal effect associated with a decrease in the use of air conditioning & not because of long-term decline in the use of electrical power. In fact, after adjusting for seasonal effect, we might even find that the use of electric power has increased.
Removing the seasonal effect from a time series is known as deseasonalising the time series. After we do so, period to period comparisons are more meaningful and can help identify whether a trend exists.

13. Using Trend and Seasonal Components in Forecasting

14. Using Trend and Seasonal Components in Forecasting
The following is a suggested approach:
Compute Centered Moving Average
Obtain Seasonal Index
Obtain deseasonalised sales
Use deseasonalised sales data to obtain trend using regression analysis.
Use seasonal index to adjust trend projection.

15. Three Variable Regression Model