Descriptive Statistics - Real Estate Data Part 1 Learning Team C QNT/351 March 28th 2016 Mike Yensz Team C has created a spreadsheet based on single family homes located in the city of Albany, NY 11207. Our research reflects property address, listing price, square footage and number of bedrooms for each listing. 46 East 22nd Street, Apt. PHB 2 West 72nd Street, Apt. 84 161 West 57th Street, Apt. 52B 4 West 72nd Street, Apt. 84 160 West 57th Street, Apt. 52B 48 East 22nd Street, Apt. PHB 3 West 72nd Street, Apt. 84 4 West 72nd Street, Apt. 84 159 West 57th Street, Apt. 52B 5 West 72nd Street, Apt. 84 47 East 22nd Street, Apt. PHB 3 West 72nd Street, Apt. 84 48 East 22nd Street, Apt. PHB 47 East 22nd Street, Apt. PHB 49 East 22nd Street, Apt. PHB 157 West 57th Street, Apt. 52B 38-40 East 75th Street 232-236 North 12th Street 232-236 North 12th Street 232-236 North 12th Street 232-236 North 12th Street 232-236 North 12th Street 34 PARK PLACE, Apt. 78A 232-236 North 12th Street 38-40 East 75th Street 232-236 North 12th Street 38-40 East 75th Street 232-236 North 12th Street 232-236 North 12th Street 232-236 North 12th Street 33 PARK PLACE, Apt. 78A 32 PARK PLACE, Apt. 78A 159 West 57th Street, Apt. 52B 158 West 57th Street, Apt. 52B 232-236 North 12th Street 232-236 North 12th Street 1 Central Park South, Apt. 1809 30 PARK PLACE, Apt. 78A 2 2 $60,000,000.00 $61,000,000.00 5,671 5,701 17 1 3 3 2 2 $80,000,000.00 $82,000,000.00 5,819 5,777 3 1 8 8 2 2 2 2 $83,000,000.00 $83,000,000.00 $84,000,000.00 $84,000,000.00 5,779 5,819 5,717 5,821 1 2 1 2 8 7 7 6 2 2 2 2 3 3 3 $85,000,000.00 $85,000,000.00 $89,000,000.00 $89,000,000.00 $81,000,000.00 $83,000,000.00 $84,000,000.00 5,719 5,817 5,759 5,671 5,775 5,715 5,815 1 3 1 16 1 1 3 6 5 7 6 8 6 5 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 $60,000,000.00 $65,000,000.00 $66,000,000.00 $74,000,000.00 $80,000,000.00 $80,000,000.00 $81,000,000.00 $81,000,000.00 $82,000,000.00 $82,000,000.00 $82,000,000.00 $83,000,000.00 $83,000,000.00 $83,000,000.00 $84,000,000.00 $84,000,000.00 $86,000,000.00 5,687 5,667 5,669 5,671 5,709 5,671 5,829 5,821 5,713 5,799 5,817 5,671 5,801 5,813 5,671 5,781 5,667 1 7 7 15 1 14 1 1 1 1 2 13 1 3 12 1 6 2 1 1 1 7 6 7 6 7 6 5 5 4 3 4 3 5 4 $86,000,000.00 5,807 1 4 4 4 4 $87,000,000.00 $88,000,000.00 $88,000,000.00 5,671 5,671 5,667 11 10 5 4 11 10 5 5 $58,000,000.00 $61,000,000.00 5,665 5,689 1 1 1 2 Summary from the Histogram The $70 are the least Occupied category of Houses. Bargraph No of bedrooms Frequency 2 12 3 2 4 21 5 10 6 16 7 13 8 7 9 4 10 4 Frequecncy Distribution Table Class 53-57 58-62 63-67 68-72 73-77 78-82 83-87 88-92 93-97 x f 55 60 65 70 75 80 85 90 95 fx 0 11 7 1 2 25 30 19 0 Based upon this data we can conclude that the majority of homes within Albany are priced within $60,000,000.00 to $84,000,000.00 range. Mean Mode Median What we see represented here is the Mean, Mode, and Median for the 100 homes. The three categories are expressed for both price and Square foot per home. When looking at the mean or the average cost over all 100 homes we see that $79,969.072 is the overall average cost. When looking at the Mode or the most commonly seen price we find that $58,000,000.00 is the most common seen price. When looking at the Median or the price of homes that is in the center we find $80,000,000.00 is the number. Now calculating the same way for square foot of the properties, we find as follows. The mean or the average square foot in the 100 homes is 5741overall. Looking at the mode, the most frequent square foot is 5671 square feet. Finally, when looking at the Median we find 5733 square feet to be in the middle. When calculating for square foot for the properties, we found the following. The mean or average square foot in the 97 homes is 2235 overall. Looking at the mode, the most frequent square foot is 556 square feet. The median is where 50% are smaller and 50% larger we find 1400 sq feet. When it comes to the empirical rule (68%-95%-99.7%) for our observed data of 100 homes which would be located on the x axis, this rule only applies to symmetrical data. \"The Empirical Rule is an approximation that applies only to data sets with a bellshaped relative frequency histogram. It estimates the proportion of the measurements that lie within one, two, and three standard deviations of the mean.\" UC Davis StatWIKI (2016). The Empirical and Chebyshev's Theorem. \"The Chebyshev's Theorem is a fact that applies to all possible data sets. It describes the minimum proportion of the measurements that must lie within one, two, or more standard deviations of the mean.\" After reviewing both descriptions of the Empirical rule and the Chebyshev's Theorem, it is believed the Empirical rule applies to the statistics gathered on the 100 houses. The shape of the distribution is what brought us to this conclusion. We feel we have a higher chance of our predictions and percentages using Empirical instead of Chebyshev's. Overall based on the actual data we have determined that three quarters of the bedroom lie between the quartile market demands. Almost two thirds of the prices lie within the first quarter price range. All the data, both price and room numbers follow distribution, therefore all lie within the 1st and third quartile. Listing price. Square footage Square footage Variance Listing price Variance $60,000,000.00 5,671 4124.195017 $88,176,116,838,488.0 0 References: UC Davis Stat Wiki, (2016) The Empirical rule and Chebyshev's Theorem. Retrieved from http://statwiki.ucdavis.edu/Textbook_Maps/General_Statistics/Shafer_and _Zhang's_Introductory_Statistics/02%3A_Descriptive_The_Empirical_Rule_and_ Chebyshev's_Theorem (empty) 46 East 22nd Street, Apt. PHB 2 West 72nd Street, Apt. 84 161 West 57th Street, Apt. 52B 4 West 72nd Street, Apt. 84 160 West 57th Street, Apt. 52B 48 East 22nd Street, Apt. PHB 3 West 72nd Street, Apt. 84 4 West 72nd Street, Apt. 84 159 West 57th Street, Apt. 52B 5 West 72nd Street, Apt. 84 47 East 22nd Street, Apt. PHB 3 West 72nd Street, Apt. 84 48 East 22nd Street, Apt. PHB 47 East 22nd Street, Apt. PHB 49 East 22nd Street, Apt. PHB 157 West 57th Street, Apt. 52B 38-40 East 75th Street 232-236 North 12th Street 232-236 North 12th Street 232-236 North 12th Street 232-236 North 12th Street 232-236 North 12th Street 34 PARK PLACE, Apt. 78A 232-236 North 12th Street 38-40 East 75th Street 232-236 North 12th Street 38-40 East 75th Street 232-236 North 12th Street 232-236 North 12th Street 232-236 North 12th Street 33 PARK PLACE, Apt. 78A 32 PARK PLACE, Apt. 78A 159 West 57th Street, Apt. 52B 158 West 57th Street, Apt. 52B 232-236 North 12th Street 232-236 North 12th Street 1 Central Park South, Apt. 1809 30 PARK PLACE, Apt. 78A 38-40 East 75th Street 38-40 East 75th Street 4 Central Park South, Apt. 1809 3 Central Park South, Apt. 1809 32 PARK PLACE, Apt. 78A 2 Central Park South, Apt. 1809 31 PARK PLACE, Apt. 78A 38-40 East 75th Street 7 East 67th Street 232-236 North 12th Street 31 PARK PLACE, Apt. 78A 45 East 22nd Street, Apt. PHB 232-236 North 12th Street 47 East 22nd Street, Apt. PHB 46 East 22nd Street, Apt. PHB 232-236 North 12th Street 33 PARK PLACE, Apt. 78A 232-236 North 12th Street 9 East 67th Street 232-236 North 12th Street 10 East 67th Street 8 East 67th Street 232-236 North 12th Street 32 PARK PLACE, Apt. 78A 3 Pierrepont Place 232-236 North 12th Street 1 West 72nd Street, Apt. 84 1050 Fifth Avenue, Apt. 18FLR 232-236 North 12th Street 1052 Fifth Avenue, Apt. 18FLR 6 Pierrepont Place 3 West 72nd Street, Apt. 84 2 West 72nd Street, Apt. 84 5 Pierrepont Place 232-236 North 12th Street 1051 Fifth Avenue, Apt. 18FLR 4 Pierrepont Place 1 West 72nd Street, Apt. 84 38-40 East 75th Street 38-40 East 75th Street 4 West 72nd Street, Apt. 84 38-40 East 75th Street 2 2 2 2 2 2 2 2 2 2 2 2 3 3 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 5 5 5 5 5 5 5 5 5 5 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 7 7 7 7 7 7 7 7 7 7 7 7 7 8 8 8 8 8 $60,000,000.00 $61,000,000.00 $80,000,000.00 $82,000,000.00 $83,000,000.00 $83,000,000.00 $84,000,000.00 $84,000,000.00 $85,000,000.00 $85,000,000.00 $89,000,000.00 $89,000,000.00 $81,000,000.00 $83,000,000.00 $84,000,000.00 $60,000,000.00 $65,000,000.00 $66,000,000.00 $74,000,000.00 $80,000,000.00 $80,000,000.00 $81,000,000.00 $81,000,000.00 $82,000,000.00 $82,000,000.00 $82,000,000.00 $83,000,000.00 $83,000,000.00 $83,000,000.00 $84,000,000.00 $84,000,000.00 $86,000,000.00 $86,000,000.00 $87,000,000.00 $88,000,000.00 $88,000,000.00 $58,000,000.00 $61,000,000.00 $81,000,000.00 $82,000,000.00 $83,000,000.00 $86,000,000.00 $87,000,000.00 $88,000,000.00 $88,000,000.00 $88,000,000.00 $59,000,000.00 $62,000,000.00 $63,000,000.00 $67,000,000.00 $82,000,000.00 $84,000,000.00 $85,000,000.00 $85,000,000.00 $86,000,000.00 $87,000,000.00 $87,000,000.00 $88,000,000.00 $88,000,000.00 $89,000,000.00 $89,000,000.00 $90,000,000.00 $60,000,000.00 $63,000,000.00 $68,000,000.00 $79,000,000.00 $80,000,000.00 $80,000,000.00 $80,000,000.00 $85,000,000.00 $86,000,000.00 $88,000,000.00 $88,000,000.00 $88,000,000.00 $90,000,000.00 $61,000,000.00 $73,000,000.00 $81,000,000.00 $81,000,000.00 $88,000,000.00 5,671 5,701 5,819 5,777 5,779 5,819 5,717 5,821 5,719 5,817 5,759 5,671 5,775 5,715 5,815 5,687 5,667 5,669 5,671 5,709 5,671 5,829 5,821 5,713 5,799 5,817 5,671 5,801 5,813 5,671 5,781 5,667 5,807 5,671 5,671 5,667 5,665 5,689 5,711 5,811 5,845 5,785 5,809 5,671 5,743 5,669 5,667 5,691 5,705 5,671 5,843 5,803 5,743 5,783 5,825 5,669 5,787 5,811 5,847 5,671 5,745 5,743 5,669 5,667 5,671 5,707 5,813 5,827 5,811 5,805 5,671 5,789 5,667 5,745 5,671 5,671 5,669 5,815 5,813 5,669 17 1 3 1 1 2 1 2 1 3 1 16 1 1 3 1 7 7 15 1 14 1 1 1 1 2 13 1 3 12 1 6 1 11 10 5 1 1 1 3 1 1 1 9 3 6 4 1 1 8 1 1 2 1 1 5 1 2 1 7 2 1 4 3 6 1 2 1 1 1 5 1 2 1 4 3 3 2 1 2 3 Frequecncy Distribution Table 3 8 Class x f fx 8 53-57 55 0 8 58-62 60 11 7 63-67 65 7 7 68-72 70 1 6 73-77 75 2 6 78-82 80 25 5 83-87 85 30 7 88-92 90 19 6 93-97 95 0 8 6 5 Frequency Polygon 2 35 1 30 1 1 25 7 6 20 7 15 6 7 10 6 5 5 5 0 55 60 65 70 75 80 4 3 4 3 Histogram 5 4 4 35 11 10 30 1 25 2 20 5 Frequency 15 4 2 10 3 5 3 0 9 55 60 65 70 75 80 8 Bin 7 1 3 3 Summary from the Histogram 1 3 The $70 are the least Occupied category of Houses. 2 4 Bargraph 3 No of bedr Frequency 2 2 12 2 3 2 1 4 21 6 5 10 5 6 16 5 7 13 4 8 7 2 9 4 1 10 4 2 1 1 5 4 3 2 21 1 4 16 3 13 Frequency 12 2 10 1 1 2 1 2 3 4 5 6 7 4 Number of Bedrooms 3 1 85 90 95 Histogram Frequency 85 90 95 Bar Graph showing the frequency of the number of bedrooms 7 4 8 4 9 10 3 West 72nd Street, Apt. 84 2 West 72nd Street, Apt. 84 7 East 67th Street 158 West 57th Street, Apt. 52B 8 East 67th Street 10 East 67th Street 160 West 57th Street, Apt. 52B 159 West 57th Street, Apt. 52B 9 East 67th Street 3 Pierrepont Place 5 Pierrepont Place 4 Pierrepont Place 6 Pierrepont Place 232-236 North 12th Street 232-236 North 12th Street 232-236 North 12th Street 232-236 North 12th Street Property address 8 8 9 9 9 9 9 9 9 10 10 10 10 11 11 11 11 Number of Bedrooms 5,791 $89,000,000.00 5,731 $91,000,000.00 5,671 $62,000,000.00 5,703 $62,000,000.00 5,733 $80,000,000.00 5,815 $82,000,000.00 5,823 $85,000,000.00 5,671 $89,000,000.00 5,793 $89,000,000.00 5,675 $63,000,000.00 5,795 $80,000,000.00 5,667 $81,000,000.00 5,817 $83,000,000.00 5,677 $64,000,000.00 5,797 $81,000,000.00 5,669 $82,000,000.00 5,819 $84,000,000.00 Listing price. Square footage frequency Chebyshev's Theorem The three quarter of the bedrooms lies between the quartiles of the market demands. Almost 2 thirds of the prices lie within the first quarter of the price ranges. Empirical Rule All the data, both price and the room numbers follow the normal distribution, therefore all lie within the 1 st and third quartile. 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 1 2 1 2 2 1 2 1 1 1 2 1 1 1 1 1 Square footages Mean 5,741 Mode 5671 Median 5,733 1st Quartil 5671 3nd Quarti 5810 prices $ 79,969,072.16 $ 58,000,000.00 $ 83,000,000.00 $ 80,000,000.00 $ 87,000,000.00 Real Estate Regression Exercise QNT/351 Version 5 University of Phoenix Material Real Estate Regression Exercise Directions: Use the real estate data you used for your Week 2 learning team assignment. Analyze the data and explain your answers. You are consulting for a large real estate firm. You have been asked to construct a model that can predict listing prices based on square footages for homes in the city you've been researching. You have data on square footages and listing prices for 100 homes. 1. Which variable is the independent variable (x) and which is the dependent variable (y)? 2. Click on any cell. Click on InsertScatterScatter with markers (upper left). To add a trendline, click ToolsLayoutTrendlineLinear Trendline Does the scatterplot indicate observable correlation? If so, does it seem to be strong or weak? In what direction? 3. Click on DataData AnalysisRegressionOK. Highlight your data (including your two headings) and input the correct columns into Input Y Range and Input X Range, respectively. Make sure to check the box entitled \"Labels\". (a) What is the Coefficient of Correlation between square footage and listing price? (b) Does your Coefficient of Correlation seem consistent with your answer to #2 above? Why or why not? (c) What proportion of the variation in listing price is determined by variation in the square footage? What proportion of the variation in listing price is due to other factors? (d) Check the coefficients in your summary output. What is the regression equation relating square footage to listing price? Copyright 2016 by University of Phoenix. All rights reserved. 1 Real Estate Regression Exercise QNT/351 Version 5 (e) Test the significance of the slope. What is your t-value for the slope? Do you conclude that there is no significant relationship between the two variables or do you conclude that there is a significant relationship between the variables? (f) Using the regression equation that you designated in #3(d) above, what is the predicted sales price for a house of 2100 square feet? Copyright 2016 by University of Phoenix. All rights reserved. 2