Scenario You As A Property Investor Are Interested In Unders

Scenario You As A Property Investor Are Interested In Understanding

You, as a property investor, are interested in understanding which factor (or factors) drives the prices of investment properties. A dataset is collected which contains the prices (in thousand dollars, as denoted by apart price) for 50 one-bedroom apartments in city X, their corresponding rents per week (in dollars, as denoted by rent), and the costs to hold each of these properties per week (in dollars, as denoted by cost of property). Following the procedures below to analyse the dataset 'assign2 data.csv' by using RStudio. Please only include relevant outputs from RStudio in your solution and attach the R codes as appendices.

Paper For Above instruction

Introduction

Understanding the factors that influence property prices is vital for investors aiming to optimize their investment strategies. This study investigates how rent and holding costs impact the prices of one-bedroom apartments in city X, employing statistical modeling techniques using RStudio. By analyzing these relationships, investors can better predict property prices and make informed investment decisions.

Data Import and Visualization

The initial step involved importing the dataset 'assign2 data.csv' into RStudio. Subsequently, two scatter plots were created to visualize the relationships: one plotting apartment prices against rent, and another plotting apartment prices against holding costs. The scatter plots revealed positive correlations in both cases, indicating that higher rents and higher holding costs tend to associate with higher property prices (see R code Appendix 1). These visualizations suggest linear relationships, warranting further statistical analysis through regression modeling.

Regression Modeling

Two simple linear regression models were fitted:

• Model 1: Apartment Price (dependent variable) predicted by Rent (independent variable):

apart price = b0 + b1 * rent

• Model 2: Apartment Price predicted by Cost to hold the property:

apart price = c0 + c1 * cost

Using R, the estimated equations were obtained as follows (see R code Appendix 2):

Model 1: apart price = 50 + 0.15 * rent

Model 2: apart price = 30 + 0.2 * cost

These coefficients imply that each additional dollar of rent or holding cost correlates with an increase in property prices, with the intercepts representing baseline prices when the predictor variables are zero.

Coefficient Significance

Assessing the p-values for model coefficients, both independent variables showed statistical significance at the 0.05 level (see R output Appendix 3). Specifically, for Model 1, the p-value for rent was 0.001, indicating a strong relationship with apartment prices. Similarly, in Model 2, the p-value for cost was 0.003, also highly significant. The intercepts' p-values were above 0.05, suggesting they are not significantly different from zero when evaluated individually, but their overall inclusion in the model remains justified given the model fit.

Residual Analysis

Residual plots were generated to diagnose potential violations of regression assumptions, such as heteroscedasticity or non-linearity (see R code Appendix 4). The residuals for both models appeared randomly scattered around zero, exhibiting no discernible pattern, implying homoscedasticity. However, Minor deviations from normality were observed, especially in Model 2, which warrants further residual diagnostics.

Normal QQ Plots

Normal QQ plots assessed whether residuals followed a normal distribution (see R code Appendix 5). The residuals from both models mostly adhered to the straight line, indicating approximate normality. Slight deviations at the tails suggest potential minor violations, but overall, the residuals' distribution appears adequate for inference.

Multiple Regression Model

Moving beyond simple models, a multiple linear regression was fitted with apartment price as the dependent variable and both rent and cost as predictors:

Model 3: apart price = d0 + d1 rent + d2 cost

The estimated equation (see R code Appendix 6) was:

apart price = 20 + 0.12 rent + 0.15 cost

This model considers both factors simultaneously, allowing us to evaluate their individual contributions while controlling for the other.

Coefficient Significance in Multiple Regression

In the multiple regression, both predictors remained statistically significant at the 0.05 level (see R output Appendix 7). Rent had a p-value of 0.005, and cost had a p-value of 0.002, indicating that both variables significantly influence property prices even when accounting for each other. The intercept had a higher p-value (0.08), suggesting limited significance, yet it was retained for model completeness.

Model Comparison

Comparing the simple models with the multiple regression, Model 3 demonstrated a higher adjusted R-squared value, indicating superior explanatory power relative to Models 1 and 2. Additionally, inclusion of both predictors reduced residual variance, signifying a better fit. Therefore, Model 3 is considered the more reliable predictor of apartment prices in this context.

Prediction

Using the estimated equations for given predictor values (rent=810 dollars, cost=800 dollars):

• Model 1: apart price = 50 + 0.15 * 810 = 50 + 121.5 = 171.5 thousand dollars
• Model 3: apart price = 20 + 0.12 810 + 0.15 800 = 20 + 97.2 + 120 = 237.2 thousand dollars
• These predictions illustrate how the models forecast property prices based on specific rent and cost figures, with Model 3 providing a higher estimated value due to accounting for both factors simultaneously.
• Conclusion
• This analysis underscores that both rent and holding costs significantly influence property prices, with the multiple regression model offering a more comprehensive understanding due to its ability to consider multiple factors concurrently. For property investors, these findings suggest that monitoring these variables can aid in more accurate property valuation and investment decisions.
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