Please provide a response to discussion post. Response must be at least 200 words.

1st post: Correlation is a relationship between two or more variables (Ravid, 2020). In statistics, correlation is described using a correlation coefficient that could assume values from -1 (perfect negative correlation) to +1 (perfect positive correlation). If the correlation coefficient is 0, the two variables are unrelated. A positive correlation indicates that an increase in values of one variable is associated with an increase in the values of another variable. A negative correlation refers to an increase in values in one variable accompanied by a decrease in values for another variable. In addition, a correlation could be negligible to low (0.00 to 0.2), low (0.20-0.40), moderate (0.40 to 0.60), high (0.60-0.80), or very high (0.80 to 1.00). A strong correlation could be visible in the scattergram due to points clustered closer to form a clear pattern. Conversely, the points spread far apart would display a weak correlation, though the pattern is still visible. 

            In my opinion, strong positive or negative correlations occur in the natural world. For example, a strong negative correlation exists between a person’s age and expected years of life. The older we get, the less years we have to live. The study by Stryzhak (2020) analyzing 145 countries shows a moderate to strong positive correlation between education (Education Index), happiness (Happiness Index), and economic freedom (Index of Economic Freedom) (See Table 1). For example, the relationship between education and happiness was 0.77 (p<0.05). 

Note. Reprinted from Stryzhak, 2020. HI – Happiness Index, 

EF – Index of Economic Freedom, FIW – Economic Freedom 

of the World Index

            Finding strong correlations in educational or medical fields could be complicated; however, even weak correlations could have practical significance. For example, the scientists found a weak correlation between PSA and prostate cancer (Ritter, 2014). It had practical significance because doctors could screen male patients for prostate cancer using PSA levels. 

Ritter (2014) explained that correlations could have practical significance if correlation could happen frequently in the future, and the benefits of acting on correlation outweigh the risks (See Figure 1). Regardless of the correlation strength, it is essential to understand its practical significance. For example, scientists found a correlation between buying red meat and lower car insurance rates, but it does not necessarily mean that people who eat more red meat and drink more milk are better drivers (Ritter, 2014).

Note. Reprinted from Ritter, 2024. 

            Correlation only indicates the relationship between two variables, or tendency of one variable to change when another variable changes, which is not a causal relationship. The reasons for that are: 

(1) possible omitted variable – some other variable that causes correlated variables to move in the same or opposite direction, 

(2) reverse causality – we do not know which of two variables causes another variable to move, (3) the sample is not representative of the population, and 

(4) measurement error – variables are not easy to measure (for example, people are not telling the truth). (Lee, 2021)

2nd Post: Correlation addresses the relationship between two variables, while regression models or predicts how the change in one variable (x) will affect the values of another variable (y) (Zach, 2021). The X variable is the predictor variable, and the Y variable is the response variable. To understand the regression values, we should consider the regression equation: 

ŷ = b0 + b1 x

Where:

ŷ: The predicted value of the response variable

b0: The y-intercept (the value of y when x is equal to zero)

b1: The regression coefficient (the average increase in y for one increase in x)

x: The value of the predictor variable

Figure 1 illustrates simple linear regression. 

Figure 1

Simple Linear Regression 

For example, if we want to predict how the number of hours studying for the exam affects exam scores, we could create a data set where the first column shows the number of hours studied and the second column shows corresponding exam scores (Figure 2). Using a regression calculator, we could calculate that:

ŷ (predicted exam score) = b0 (65.1) + b1 (2.5) x(hours studied)

This equation shows that students who did not study for the exam would get a score of 65.1. Each additional hour of study will increase the predicted score by 2.5. 

            Both correlation and simple linear regression show the direction and strength of the relationship between two variables. Regression also (1) predicts how the change in one variable will affect another variable and (2) uses an equation to predict the value of one variable based on another variable. 

            In simple linear regression, only one predictor and one response variable are used (
Linear regression versus multiple regression, 2021). In multiple linear regression, there are multiple predictors but only one response variable. The multiple linear regression equation looks like this: 

Multiple linear regression is used to evaluate the extent to which two or more predictor variables are related to the response variable and to predict the value of the response variable based on values of predictor variables. Multiple regression could be used in planning, monitoring, predicting, and forecasting. In research, multiple regression analysis evaluates how each predictor variable contributes to the relationship.

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