Advantages of Multivariate Analysis

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Advantages of

Multivariate

Analysis

Close resemblance to how the researcher thinks.

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Easy visualisation and interpretation of data.

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More information is analysed simultaneously, giving greater power.

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Relationship between variables is understood better.

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Focus shifts from individual factors taken singly to relationship among variables.

Definitions - I

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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

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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.

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Scatterplot of deuterium against testweighing

Deuterium = -67.3413 + 1.16186 Test weigh

S = 234.234 R-Sq = 59.3 % R-Sq(adj) = 56.0 %

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Test weigh

Regression

95% CI

Definitions - III

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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

Intercept

Slope

X axis

Basic Assumptions

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Y increases or decreases linearly with increase or decrease in X.

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For any given value of X the values of Y are distributed Normally.

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Variance of Y at any given value of X is the same for all value of X.

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The deviations in any one value of Y has no effect on other values of Y for any given X

The Residuals

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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

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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 - S yy

Analysis of Variance - II

Total Sum of Squares ( S yy

) 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

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Regression Equation

Residual Sum of Squares (RSS)

Values of α and β.

R

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S (standard deviation)

Testing for β ≠ 0

Analysis of Variance Table

F test

Outliers

Remote from the rest

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