# Quiz Correlation & Regression

This Post contains Quiz Correlation Regression Analysis, Multiple Regression Analysis, Coefficient of Determination (Explained Variation), Unexplained Variation, Model Selection Criteria, Model Assumptions, Interpretation of results, Intercept, Slope, Partial Correlation, Significance tests, OLS Assumptions, Multicollinearity, Heteroscedasticity, Autocorrelation, graphical representation of the relationship between the variables, etc. Let us start with Quiz Correlation Regression Analysis.

Correlation analysis is a statistical measure used to determine the strength and direction of the mutual relationship between two quantitative variables. The value of the correlation lies between $-1$ and $+1$. The regression analysis describes how an explanatory variable is numerically related to the dependent variables.

The formula to compute the correlation coefficient is:

$$r = \frac{n\sum X_i Y_i – \sum X_i \sum Y_i}{\sqrt{[n\sum X_i^2 – (\sum X_i)^2][n\sum Y_i^2 – (\sum Y_i)^2]}}$$

The general regression equation is $Y_i = a + bX_i$. The slope coefficient and intercept of the regression model can be computed as

\begin{align*} b &= \frac{n\sum X_i Y_i – \sum X_i \sum Y_i}{n\sum X_i^2 – (\sum X_i)^2}\\ a &= \overline{Y} – b\overline{X} \end{align*}

Both of the tools are used to represent the linear relationship between the two quantitative variables. The relationship between variables can be observed using a graphical representation between the variables. We can also compute the strength of the relationship between variables by performing numerical calculations using appropriate computational formulas.

Note that neither regression nor correlation analyses can be interpreted as establishing some cause-and-effect relationships. Both correlation and regression are used to indicate how or to what extent the variables under study are associated (or mutually related) with each other. The correlation coefficient measures only the degree (strength) and direction of linear association between the two variables. Any conclusions about a cause-and-effect relationship must be based on the judgment of the analyst.

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