Real Estate Growth Rates

A Comparison of Gardnerville/Minden and Carson City Areas

By

Amy Smith

The purpose of this project is to evaluate the real estate growth in the Gardnerville/Minden, NV area versus real estate growth in the Carson City, NV area over the past ten years.  Both areas have experienced rapid growth over the past decade however it is believed that the mean growth rates are not equal.  The null hypothesis is that the growth in Gardnerville/Minden, NV is equal to that of Carson City, NV.  The alternative hypothesis is that the growth rates are not equal and that one is greater than the other.  To determine the growth rates we will use the number of homes sold over the past ten years and compute statistical analysis on the data with alpha equal to 95%.

Furthermore, analysis of the mean home price for both real estate areas will be calculated to determine if there is any correlation between mean home price and growth rate.  The data listed for these calculations comes from the multiple listing service stats of single family homes and was obtained from the Sierra Nevada Association of Realtors located at 300 South Curry Street #3 in Carson City, NV 89703.

The following data table shows the number of homes sold in Gardnerville/Minden area and the number of homes sold in the Carson City area over the past ten years.

Provided below are histograms which represent the frequency distribution of the data points in the above chart. 

            In Gardnerville/Minden, the highest frequency of homes sold is around 784 per year and greater than 968 sold per year.  The frequency distribution for homes sold in Gardnerville/Minden is bi-modal and slightly

skewed right.

            In Carson City, the highest frequency of homes sold is around 574 per year and greater than 693 homes sold per year.  The frequency distribution for homes sold in Carson City is bi-modal and slightly skewed right.

The following pie chart represents the total number of homes sold from 1993-2003 and the distribution of those homes sold.  There were 15,670 homes sold from 1993-2003 – 57% of those homes sold were located in Gardnerville/Minden areas and 43% of the homes sold were located in the Carson City area.

In order to analyze this data I have provided a descriptive statistic chart of homes sold for each real estate area.

From the given data table the mean number of homes sold per year in Gardnerville/Minden is 816 homes with a standard deviation of approximately 175.  The mean number of homes sold per year in Carson City is 608 with a standard deviation of approximately 140.  The average number of homes sold per year is greater in Gardnerville/Minden area than it is in the Carson City area.  The bar chart below compares the number of homes sold in Gardnerville/Minden vs. Carson City.

                    From the data given above, it is clear that the number of homes sold in Gardnerville/Minden is greater than the number of homes sold in Carson City over the past 10 years.  Now we need to look at the growth rate in number of homes sold for both locations to determine which is higher.  To determine the growth rate we will look at the percentage of homes sold in previous years and compare the percentages for each location.  The following data table shows the number of homes sold in each location compared to the previous year.

           The average difference of homes sold from previous year in the Gardnerville/Minden area is 43 homes.  More specifically, this means that over the past ten years there has been an average growth of 43 more homes sold per year in Gardnerville/Minden.  The average difference of homes sold from previous years in the Carson City area is 24 homes, which means that on average there is an increase of 24 homes sold per year.  Below is a line chart to visually represent this data.

            In order to determine growth rates, we will examine the percentage of real estate growth in each area.  By looking at percent of real estate growth we will be able to determine if there is enough change in percentage of growth per year to determine whether or not one area is growing at a more rapid rate than the other.  The following table lists the data.

The mean real estate growth percentage for Gardnerville/Minden is 6.56% per year for the past ten years.  Additionally, the mean real estate growth percent for Carson City is 5.81% per year for the past ten years.  Gardnerville/Minden has a higher mean growth percentage rate than Carson City, however, this does not mean that we can reject the null hypothesis and accept the alternative hypothesis.  Statistical analysis must be done to determine if out data falls outside the critical region.  In order to correctly analyze the data a t-test for two variables need to be calculated (with alpha equal to 95%).  The table below lists the results of the t-test.

To determine whether or not to accept the alternative hypothesis we must look at the critical area for the two tail test with an alpha of 95% and see if the t score falls beyond that region.  The two tailed t-test critical region is (-) or (+) 2.1199.  The calculated t score for the data equals -.1352, which does not fall into the critical region for accepting the alternative hypothesis.  Therefore, we fail to reject the null hypothesis and conclude that the data is not statistically significant enough to accept the alternative hypothesis.  More data collection is needed and further statistical analysis should be done.

The second purpose of this project is to determine whether or not there is any correlation between growth rate and mean home price in the study areas.  The data needed to calculate this relationship is the mean home price for each year in the given area and the percent of real estate growth in each area.  The following table lists the necessary data.

            It is helpful to view the data in a scatter diagram to see if there is any correlation.  Below is the scatter diagram for Gardnerville/Minden, which shows the relationship (if any) between mean home price and growth percentage.

            The r-squared value is .1349, which indicates there is approximately a 13.40% percent that the y-value can be predicted from the given x-value.  Moreover, there is 86.51% that you can predict the y-value from a given x-value.  There might be other factors involved when trying to predict the growth percentage other than mean home price. 

            The following scatter diagram depicts the correlation (if any) between mean home price and percent of growth for Carson City.

The diagram above illustrates that there is very little correlation between the mean home price and percent growth rate for Carson City.  From the scatter chart the r-squared value is .0352, which means that there is a 3.52% that the y-value can be predicted from a given x-value.  Conversely, there is a 96.48% that the y-value cannot be predicted from a given x-value.  From this data set it cannot be concluded that there is any correlation between the mean home price and the percent growth rate in Cason City.

            In conclusion, we fail to reject our first hypothesis, in that, we cannot conclude that the real estate growth rates for Carson City and Gardnerville/Minden areas are different than one another.  Second, the data is statistically insignificant to conclude that there is any relationship between the real estate growth rates and mean home price in either study areas.  Larger samples are needed and further statistical analysis needs to be done accept either alternative hypothesis.