Statistics

Statistics week 10 assignmentName:
Institutional Affiliation
Statistics Week 10 Assignment
Traditionally, the housing industry has been quite expensive to invest in let alone acquire houses. The cost of acquiring a house has been traditionally quite high especially during the housing bubble that caused the mortgage crisis. However, the financial recession changed the industry, and the scepticism of most people has driven interest rates low. This paper provides an assessment that shows the decline in housing prices and the need to make housing purchases rather than renting.
One of the main considerations is assessing the descriptive statistics of the interest rates in the housing market. This is indicated in the following table.
Descriptive statistics for the annual interest rates
Mean 8.472790698
Standard Error 0.470107234
Median 8.04
Mode #N/A
Standard Deviation 3.082699285
Sample Variance 9.503034884
Kurtosis 0.547788967
Skewness0.81869509
Range 12.97
Minimum 3.66
Maximum 16.63
Sum 364.33
Count 43
Confidence Level(95.0%) 0.948714807
The outcome shows that the mean annual interest rate is 8.472790698 percent with a median rate of 8.04 percent. There is no mode for the data because none of the values has appeared more than once. The standard deviation is 3.082699285 from a 9.503034844 variance. The data has a 0.81869509 skewness indicating that the data is skewed to the right.
The next step is the construction of 95 percent confidence interval.
The formulae to calculate the confidence interval is given by

Where the average is 8.472791, the 95% confidence coefficient is 1.96, the standard deviation is 3.082699, and the sample size is 43.

= (7.551381, 9.394201)Another consideration is determining how many standard deviations from the mean is the interest rate in 2014.
The following formulae give the calculation for the standard deviation of a fixed point in a sample.

Another important consideration is the trend of the data.

A linear trend line indicates that there has been a decline in the interest rates.

A moving average trendline indicates that in the future there will be an increase in the mortgage rates, so the company needs to take advantage of the low-interest rates.
Based on the data provided, a prediction can be made about the interest rate in 2015 and 2016.
The most important part is determining the regression equation. This can be done either using the full regression or estimating using a simple linear regression intercept and slope. The latter is the easiest in making predictions. The simple linear regression model used is given as:

The main things that need to be determined are the coefficients for the intercept and the slope based on the equation.

The prediction for 2015 is 4.5534
The prediction for 2016 is 4.37522
The information provided in the study indicates that there is a decrease in the annual mortgage interest rates. The low-interest rates are only marginally higher than the renting prices. The annual interests are normally at around the mean of 8.472790698. The interest rate in 2014 is only 4.17. This is standard deviations below the mean. In addition to this, the moving average indicates that there will be an increase in the annual interest rates in the future. This is a situation where the market forces are about to change to another increase in annual interest rates.
Investing in acquisition at this time will allow the organization to get assets at almost the same value as renting. In addition to this, the acquisition will provide an asset on the balance sheet that can be used in leveraging for loans in cases of financial imbalances in the future. This will allow the organization to house more people with the limited resources available. The main important measure that needs to be ensured is selecting fixed mortgage rates rather than adjustable mortgage rates. This will ensure that the same mortgage premiums will be paid regardless of the expected increase in annual interest rates.