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## PowerPoint Slideshow about 'Advantages of Multivariate Analysis' - ostinmannual

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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.

Definitions - I

- 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

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.

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

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

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

Analysis of Variance - I

- The variation of Y values around the regression line is a measure of how X and Y relate to each other.
- Method of quantifying the variation is by Analysis of variance presented as Analysis of Variance table
- Total sum of squares represents total variation of Y values around their mean - Syy

Analysis of Variance - II

Total Sum of Squares ( Syy ) is made up of two parts:

(i). Explained by the regression

(ii). Residual Sum of Squares

Sum of Squares ÷ its degree of freedom = Mean Sum of Squares (MSS)

The ratio MSS due to regression ÷ MSS Residual = F ratio

Reading the output

- Regression Equation
- Residual Sum of Squares (RSS)
- Values of α and β.
- R2
- S (standard deviation)
- Testing for β≠ 0
- Analysis of Variance Table
- F test
- Outliers
- Remote from the rest

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