Relationship between two continuous variables: Correlation and Regression

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  • Created by: lewis
  • Created on: 19-04-19 22:54
Correlation ‘r’
Correlation refers to how close two variables are to having a linear relationship / the strength of their linear relationship. - ‘r’ belongs to [-1,1]
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Pearson correlation ‘r’
Correlation can be measured using the Pearson correlation coefficient ‘r’. To use a Pearson correlation, each variable must be normally distributed.
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Spearman correlation
If one or both variables are not normally distributed, then a non-parametric approach must be conducted instead. Spearman correlation between two variables is defined as the Pearson correlation after replacing data points by their ranks (order).
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Regression models
A regression model is a set of statistical processes for estimating the relationships among variables. The relationship is expressed as an equation: Term A = Term B
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In each term of the regression model equation, different variables are involved:
Term A “y “ dependent (outcome) variable. Term B ” x1, x2 ... xn “ n variables called “independent variables” (also covariates, explanatory variables, or predictor variables). IV & DV can be either continuous or categorical
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e is called
the residual.
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The intercept..
the value that y takes when x is zero. If the intercept is zero then y increases in proportion to x (i.e. double x then y doubles).
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The slope..
the change in y when x changes by one unit.
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Prediction
Regression models are used to predict new cases. The predicted value y^ for a new observation x is its corresponding value on the regression line.
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Inference: 5 Assumptions (1 & 2)
1) The relationship between the IV & DV is linear. 2) Residuals should be approximately normally distributed.
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Inference: 5 Assumptions (3, 4 & 5)
3) Homoscedasticity: Scatterplot of standardised residuals and standardised predicted values shows no pattern. 4) Independent observations 5) No observations have a large overall influence (leverage).
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Simple linear regression: when x is categorical binary then:
The regression line connects the mean response in one group with the mean response in the other. The slope coefficient simply measures the group difference in means (nb: slope measures predicted change in y when x changes by one unit=switches group
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A dummy (indicator) variable is
a binary (0,1) variable indicating a category of the predictor variable
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Other cards in this set

Card 2

Front

Pearson correlation ‘r’

Back

Correlation can be measured using the Pearson correlation coefficient ‘r’. To use a Pearson correlation, each variable must be normally distributed.

Card 3

Front

Spearman correlation

Back

Preview of the front of card 3

Card 4

Front

Regression models

Back

Preview of the front of card 4

Card 5

Front

In each term of the regression model equation, different variables are involved:

Back

Preview of the front of card 5
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