Statistical Analysis of Regional vs. National Housing Prices Using Regression Testing and Excel

Problem Description

In this Excel assignment, we aim to determine whether housing prices in the West South-Central region of the United States are lower than the national market average. Additionally, we want to assess whether the square footage of homes in the West South-Central region differs from the national market's average square footage. To accomplish this, we will utilize statistical tools, specifically the independent sample T-test. Our null hypothesis states that the means are equal, while the alternate hypothesis posits that the means are different.

Sample Data

To conduct this analysis, we collected data from various counties and states, resulting in the following information:

Counties:

• We collected data from 500 counties in the West South Central region.

States:

• We also collected data from 500 samples across six states, including Connecticut (CT), Massachusetts (MA), Maine (ME), New Hampshire (NH), Rhode Island (RI), and Vermont (VT).

Methodology:

We will employ two different tests:

1. 1-Tail Test:
• Hypothesis: We will compare housing prices in West South Central to the national market average, assuming that West South Central's prices are greater or equal to the national average.
• Data analysis: We will use the T-test, and based on our data analysis, we will determine if the null hypothesis can be rejected or not.
2. 2-Tail Test:
• Hypothesis: We will compare the square footage of homes in West South Central to the national market average, assuming that they are not equal.
• Data analysis: Similar to the 1-Tail Test, we will use a T-test to make this comparison.

Both of the tests will be conducted within a 95% confidence interval.

1-Tail Test Results:

• We found that housing prices in West South Central are skewed to the left, indicating that most houses are priced lower than the mean.

Table 1: 1-Tail Test Results (Housing Prices)

• The assumptions of a normal distribution are met because the sample size is greater than 30.
• The p-value obtained was greater than the significance level (0.5201 > 0.05). Therefore, we fail to reject the null hypothesis, concluding that housing prices in West South Central are greater or equal to the national market average.

2-Tail Test Results:

• The data on square footage for homes in West South Central showed a normal distribution, and the mean and median values were similar.

Table 2: 2-Tail Test Results (Square Footage)

• The p-value for this test was 1, which is greater than the significance level of 0.25. Thus, we fail to reject the null hypothesis, indicating that the housing square footage in West South Central is equal to the national market average.

Comparison of the Test Results:

• T-Test for Paired Two Samples for Means:

Table 3: Comparison of Test Results (Housing Prices)

• Observations = 500
• The Pearson correlation is 0.5098
• t Stat = 54.6554
• The p-value for this test was extremely low (4.4E-213), indicating a significant difference between housing prices in West South Central and the national market average.

Final Conclusions:

In summary, our analysis revealed the following findings:

• Most housing prices in West South Central are greater than the national data, as demonstrated by the 1-Tail Test.
• However, there is no major difference in square footage between homes in West South Central and the national market average, as shown by the 2-Tail Test.

This analysis serves as an example of using regression testing and Excel to compare regional and national housing market data. It provides valuable insights into regional variations in housing prices and square footage, which can be useful for real estate professionals and investors.