A brief note on correlation analysis and multiple regression analysis: for Housing Studies students

A brief note on correlation analysis and multiple regression analysis: for Housing Studies students (information from perplexity.ai)

My question 1: "Highlight the main ideas of (1) correlation analysis and (2) multiple regression analysis of Quantitative Research in the context of Housing Studies."

The reply: "Correlation analysis and multiple regression analysis are two fundamental quantitative research methods widely used in Housing Studies to understand relationships between variables and predict outcomes.

Correlation Analysis in Housing Studies

Correlation analysis measures the strength and direction of the relationship between two variables, such as housing quality and occupants' satisfaction, or housing characteristics and health outcomes. In Housing Studies, researchers often use correlation coefficients (e.g., Pearson or Spearman) to determine if changes in one variable are associated with changes in another. For example, studies have shown strong positive correlations between housing quality indicators (like floor area per capita, access to water, and electricity) and broader social indicators such as the Human Development Index. Correlation analysis helps identify which housing factors are most closely linked to outcomes of interest, but it does not establish causation—only association.​

Multiple Regression Analysis in Housing Studies

Multiple regression analysis extends correlation by allowing researchers to examine how several independent variables simultaneously influence a dependent variable, such as housing affordability or property prices. In Housing Studies, this method is used to build predictive models—for instance, estimating house prices based on factors like building area, age, location, and amenities. The regression equation quantifies the impact of each predictor, enabling researchers to identify which factors are most influential and to forecast outcomes under different scenarios. This approach is crucial for policy development, as it helps prioritize interventions that will most effectively improve housing conditions or affordability.​

Key Differences and Applications

• Correlation analysis is used to explore bivariate relationships and is often the first step in identifying which variables might be worth including in a regression model.​

• Multiple regression analysis is used for prediction and to understand the relative importance of multiple factors, providing a more nuanced view of complex housing issues.​

Both methods are essential for evidence-based decision-making in housing policy, urban planning, and real estate research, helping to clarify the factors that drive housing outcomes and inform targeted interventions."

My question 2: "Briefly explain the ideas of (1) positive and negative correlation and (2) strong and weak correlation in correlation analysis."

The reply: "Positive correlation in correlation analysis means that two variables move in the same direction: as one variable increases, the other also increases; similarly, if one decreases, the other decreases. This implies a direct relationship, often reflected by a correlation coefficient between 0 and +1.​

Negative correlation means the two variables move in opposite directions: as one variable increases, the other decreases, and vice versa. This inverse relationship is indicated by a correlation coefficient between 0 and -1.​

Strong correlation refers to a high absolute value of the correlation coefficient close to 1 (whether positive or negative), indicating a strong linear relationship between the variables, meaning one variable can reliably predict the other. Weak correlation, with a coefficient closer to 0, indicates a poor or weak linear relationship where the variables do not predict each other well.​

In summary:

• Positive correlation: variables increase or decrease together.

• Negative correlation: one variable increases while the other decreases.

• Strong correlation: correlation coefficient close to ±1.

• Weak correlation: correlation coefficient close to 0."

My question 3: "What would a correlation formula and a multiple regression formula look like with reference to the research theme of "how the unemployment rate and other factors affect the gen y couples' confidence to purchase a residential apartment in Wai Chai of Hong Kong in 2025"?"

The reply: "For the research theme "how the unemployment rate and other factors affect the Gen Y couples' confidence to purchase a residential apartment in Wai Chai of Hong Kong in 2025," the formulas for correlation and multiple regression analysis can be structured as follows:

1. Correlation formula:
   The correlation coefficient 
   $r$

$$r=\frac{\sum (X_i-\bar{X})(Y_i-\bar{Y})}{\sqrt{\sum (X_i-\bar{X}{)}^2\sum (Y_i-\bar{Y}{)}^2}}$$

where $X_i$ and $Y_i$ are individual observations of the unemployment rate and confidence, respectively, and $\bar{X}$, $\bar{Y}$ are their means.

2. Multiple regression formula:
   The multiple regression model estimates how multiple independent variables—including unemployment rate and other factors (e.g., household income, housing prices, interest rates)—collectively affect the dependent variable, confidence to purchase $Y$:

$$Y={\beta }_0+{\beta }_1(\text{Unemployment Rate})+{\beta }_2(\text{Household Income})+{\beta }_3(\text{Housing Prices})+{\beta }_4(\text{Interest Rates})+ϵ$$

• $Y$: Gen Y couples' confidence to purchase residential apartments

• ${\beta }_0$: intercept (baseline confidence level)

• ${\beta }_1,{\beta }_2,{\beta }_3,{\beta }_4$: regression coefficients indicating the effect size of each independent variable

• $ϵ$: error term capturing unexplained variation

This model quantifies how changes in unemployment and other factors impact the confidence level among Gen Y couples in Wai Chai for the year 2025.

These formulas reflect the typical statistical approach in quantitative housing studies concerning socioeconomic influences on housing market confidence."

*** a note on an example of a multiple regression formula.

A collection of blog notes on using chatgpt for research purpose.