**Parametric Pearson Correlation with Excel**

**1. Data collection**

**2011 ~ 2022: Total 11 years**

**consumer price index**

An indicator to measure price changes in goods and services purchased by consumers

**Consumer Sentiment Index (CCSI)**

It is a composite index of major individual indices (6 such as current living conditions) as a standard, and is a comprehensive consumer psychological indicator of the economic situation.

**2. Data preprocessing and processing**

Data is provided monthly, averages are calculated by year, and organized

into 11 columns each.

**3. Data visualization and analysis**

Under the assumption that both data **follow a normal distribution,** we attempted parametric methods of **Pearson correlation analysis and regression analysis** .

**Correlation analysis (r) is** used to determine whether there is **a relationship with the purpose ****(** degree of correlation between two variables, strength of relationship between changes in two variables),

Regression analysis is about seeing **how much a change in cause affects the outcome ****.**

**Correlation (r) analysis of two variables**

**Correlation (r) -0.3827** is negative (-), indicating an inverse direction.

This means that as the consumer price index rises, consumer sentiment decreases. When

the price rises by 1, consumer sentiment decreases by 0.38.

**Scatter plot trend line (linear regression line)** _ Linear relationship visualization

The linear regression line also shows a negative direction.

Regression coefficient (y) = -0.3993x + 139.63

**The coefficient of determination R^2 (14.6% _ 0.1465)** is low in that the cause affects the result.

(Although the hypothesis test is significant) this analysis has only 14.6% explanatory power.

*** Correlation coefficient (r)**

The value of r is between -1 < r < 1.

The larger the absolute value of r, the greater the linear relationship.

r < 1 Proportional (same) direction

r=0 No relationship

r < 1 Inversely proportional direction

* Depending on the normality of correlation analysis (whether it follows a normal distribution or not), it is divided into parametric and non-parametric methods.

**Parametric method** : When following normal distribution ( T test, analysis of variance (ANOVA), Pearson’s correlation analysis)

**Non-parametric method** : When normal distribution is not followed or normal distribution cannot be assumed ( Spearman’s rank correlation analysis, Mann-Whitney test, Wilcoxon signed rank test, Kruskal-Wallis test)

*** Coefficient of determination r^2**

The value of r^2 is between 0 < r <= 1.

The closer the value is to 1, the higher the explanatory power.

If it is 1, it means that the model predicting the variable (y) in question explains all of the data.

It is used to determine the explanatory power of regression analysis, and the causality of the independent and dependent variables is determined by the interpreter.

A large coefficient of determination does not automatically mean that causality (if there is a cause, there is an effect) is large, but it can be judged that the regression model is well estimated.

**Resources**

**Consumer Price Index, Consumer Sentiment Index**

**How to use Excel Pearson correlation correlation analysis**

**Parametric and non-parametric differences explained**

**Pearson correlation analysis (Pearson, Spearman), regression analysis explanation**

**Difference between correlation coefficient and coefficient of determination**

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