Advantages of Multivariate Analysis

1
Advantages of Multivariate Analysis

• Close resemblance to how the researcher thinks.
• Easy visualisation and interpretation of data.
• More information is analysed simultaneously,
  giving greater power.
• Relationship between variables is understood
  better.
• Focus shifts from individual factors taken singly
  to relationship among variables.

2
Definitions

• Independent (or Explanatory or Predictor)
  variable always on the X axis.
• Dependent (or Outcome or Response) variable
  always on the Y axis.
• In OBSERVATIONAL studies researcher observes the
  effects of explanatory variables on outcome.
• In INTERVENTION studies researcher manipulates
  explanatory variable (e.g. dose of drug) to
  influence outcome

3
Definitions - II

• Scatter plot helps to visualise the relationship
  between two variables.
• The figure shows a scatter plot with a regression
  line. For a given value of X there is a spread of
  Y values. The regression line represents the mean
  values of Y.

4
Definitions - III

• INTERCEPT is the value of Y for X 0. It
  denotes the point where the regression line meets
  the Y axis
• SLOPE is a measure of the change in the value of
  Y for a unit change in X.

Y axis
Slope
Intercept
X axis
5
Basic Assumptions

• Y increases or decreases linearly with increase
  or decrease in X.
• For any given value of X the values of Y are
  distributed Normally.
• Variance of Y at any given value of X is the same
  for all value of X.
• The deviations in any one value of Y has no
  effect on other values of Y for any given X

6
The Residuals

• The difference between the observed value of Y
  and the value on the regression line (Fitted
  value) is the residual.
• The statistical programme minimizes the sum of
  the squares of the residuals. In a Good Fit the
  data points are all crowded around the regression
  line.

Residual