D.M. Pan Real Estate Company recently hired me to help develop a model that predicts housing prices for homes sold in 2019 across the country. The CEO wants to use the report to help the real estate team develop a better predictor of house prices based on square footage. The company has provided a real estate data spreadsheet showing a sample of properties sold nationwide across all years in 2019 and they expect me to select a region, conduct analysis, and provide a report addressing their objectives. The report therefore aims at describing in detail the correlation between square footage and listing price.

Linear regression usage will be appropriate in this analysis if there is a linear relationship between the two variables or a line of best fit. This will facilitate the predictive capabilities of the model. In such an instance, the scatterplot will have clusters of size and price points populating the graph in a particular direction (positive or negative). It will clearly show the predictor and response variables. A predictor or independent variable is a factor in the relationship that can predict the value of another (the response or dependent variable). For this investigation, the predictor variable will be square footage and the response variable will be listing price.

*Random sample of 50 properties*

Region | State | County | listing price | $’s/ sqft | sqft |

South Atlantic | NC | Edgecombe | 349,400 | $170 | 2,061 |

West South Central | TX | Coryell | 184,100 | $126 | 1,460 |

Pacific | CA | Contra costa | 366,500 | $225 | 1,626 |

New England | VT | Windsor | 731,000 | $137 | 5,319 |

Mid Atlantic | MD | Baltimore city | 351,000 | $189 | 1,861 |

East South Central | AL | Baldwin | 197,100 | $120 | 1,646 |

New England | CT | Windham | 381,900 | $154 | 2,475 |

New England | ME | Penobscot | 307,400 | $177 | 1,740 |

Mountain | CO | Weld | 382,600 | $178 | 2,151 |

Northeast | PA | Erie | 229,200 | $181 | 1,263 |

Pacific | WA | Clark | 460,700 | $240 | 1,922 |

Pacific | CA | Napa | 404,100 | $228 | 1,769 |

Mountain | MT | Yellowstone | 326,000 | $198 | 1,643 |

East North Central | IL | Peoria | 187,900 | $131 | 1,434 |

Pacific | HI | Honolulu | 273,300 | $224 | 1,220 |

Northeast | NY | Saratoga | 304,600 | $157 | 1,946 |

South Atlantic | FL | Bay | 309,700 | $169 | 1,830 |

New England | MA | Essex | 391,300 | $179 | 2,183 |

East South Central | TN | McMinn | 234,900 | $108 | 2,176 |

Pacific | WA | Kitsap | 362,900 | $249 | 1,459 |

Northeast | NY | Oneida | 308,500 | $168 | 1,840 |

West South Central | LA | East baton rouge | 254,100 | $135 | 1,881 |

Northeast | NY | Wayne | 321,300 | $204 | 1,573 |

Mountain | MT | Cascade | 296,000 | $126 | 2,341 |

Mid Atlantic | VA | Rockingham | 313,400 | $210 | 1,490 |

Pacific | CA | Marin | 420,800 | $227 | 1,856 |

East North Central | IN | Vanderburgh | 214,100 | $134 | 1,596 |

Mid Atlantic | MD | Worcester | 274,400 | $226 | 1,215 |

West South Central | OK | Carter | 263,000 | $142 | 1,856 |

South Atlantic | GA | Paulding | 348,200 | $154 | 2,263 |

West North Central | MN | Sherburne | 361,600 | $177 | 2,041 |

East South Central | KY | Daviess | 239,800 | $113 | 2,118 |

Northeast | NY | Schenectady | 331,300 | $163 | 2,031 |

Mountain | MT | Lewis and Clark | 287,300 | $187 | 1,533 |

West North Central | ND | Grand forks | 394,400 | $169 | 2,338 |

West South Central | OK | Washington | 167,100 | $110 | 1,526 |

Northeast | PA | Lancaster | 248,500 | $170 | 1,465 |

West South Central | AR | Faulkner | 280,500 | $129 | 2,168 |

West South Central | TX | Nacogdoches | 630,800 | $124 | 5,107 |

Mountain | WY | Laramie | 292,500 | $202 | 1,448 |

East North Central | MI | Lenawee | 191,500 | $118 | 1,628 |

South Atlantic | SC | Orangeburg | 305,400 | $172 | 1,780 |

East North Central | MI | Shiawassee | 192,400 | $129 | 1,494 |

South Atlantic | SC | Georgetown | 371,300 | $185 | 2,006 |

Pacific | CA | Placer | 314,600 | $266 | 1,182 |

New England | MA | Plymouth | 311,000 | $183 | 1,703 |

Mountain | NV | Washoe | 357,500 | $153 | 2,336 |

Northeast | NY | Livingston | 353,400 | $220 | 1,603 |

West North Central | MN | Chisago | 309,900 | $196 | 1,583 |

Pacific | CA | Solano | 343,700 | $277 | 1,240 |

The sample data above draws from the list of 100 properties sold in the US in 2019. The analyst used the random function of MS Excel to shuffle the list and picked the first 50 houses listed as the sample for this analysis. As instructed at the start of the process, he chose the size in square feet as the predictor variable and the listing price as the response variable.

*Histograms*

For property size the shape of the graph is skewed right or positively skewed because there are many properties listed in the lower end of property size listing. The center of the graph which is the mean is therefore in the first bin or size category (1182 – 2182) because it is 1908.5 sqft. The spread which is the standard deviation is 757.2 sqft. There are two outliers in the 4182 – 5182 (5107 sqft) category and the 5182 – 6182 (5319). There is also a gap in the 3182 – 4182 where there is no listing

For listing price, the shape of the graph is bell shaped or normally distributed because there are many properties listed in the central category of 267,100 – 367,100. The center of the graph which is the mean is therefore in the second bin or listing price category (267,100 – 367,100) because it is $320,678. The spread which is the standard deviation is $100761.1. There are two outliers in the 567,100 – 667,100 ($630,800) category and the 667,100 – 767,100 (731,000). There is also a gap in the 467,100 – 567,100 category where there is no listing

*Summary sample statistics*

square feet | listing price | |

Mean | 1908.5 | 320678.0 |

Median | 1774.5 | 310450.0 |

Standard Deviation | 757.2 | 100761.1 |

*Summary national statistics*

Square feet | Listing price ($) | |

Mean | 2,111 | 342,365 |

Median | 1,881 | 318,000 |

Std. Dev. | 921 | 125,914 |

The summary sample statistics are lower than the summary national statistics in every category as observable in the tables above. Hence the sample is not representative of the national market statistics.

A regression model can be developed for the data as observable in the scatter plot above by that regresses listing price ($) against size (sqft).

From the scatterplot the association between size and price is positive, which means an increase in property size leads to an increase in listing price. The R^{2} value is at 0.6183 which means that size can predict upto 61.83% of property listing price i.e. a strong relationship.

The r value is therefore the square root of R^{2} which comes to 0.7863. This is the correlation coefficient, which indicates whether the relationship is positive or negative and how strong it is. A correlation coefficient ranges from -1 to +1 with values closest to the limits indicating strong correlation. The R-value of 0.7863 confirms that the relationship between the two is strong and positive.

*Regression equation*

y = 104.63x + 120996

The slope of the equation is 104.63 which means that for every unit increase in property size there is a 104.63 units increase in listing price. The intercept of the equation is 120,996 which means that before any property is built the average value of the land in the sample should be $120,996

The R^{2} value is at 0.6183 which means that size can predict upto 61.83% of property listing price i.e. a strong relationship.

For example, a property with a size of 2,061 sqft should cost

y = 104.63(2,061) + 120996 = $336638.43

The results above such a property (2061 sqft) is actually present in the sample in South Atlantic region, North Carolina state, Edgecombe county and goes for $349,400. This slight difference shows the accuracy of the equation and also accommodates local factors such as location, property taxes, etc. Accommodating such local factors in a set of national property listings could actually contribute to the increased accuracy of the equation, which would make predictions more focused. One question that could be interesting for follow-up research is therefore, what factors apart from property size and can accurately predict the property listing price in the US real estate market.

**References**

Flaxman, S. (2018). Predictor Variable Prioritization in Nonlinear Models with RATE.

D.M. Pan Real Estate Company recently hired me to help develop a model that predicts housing prices for homes sold in 2019 across the country. The CEO wants to use the report to help the real estate team develop a better predictor of house prices based on square footage. The company has provided a real estate data spreadsheet showing a sample of properties sold nationwide across all years in 2019 and they expect me to select a region, conduct analysis, and provide a report addressing their objectives. The report therefore aims at describing in detail the correlation between square footage and listing price.

Linear regression usage will be appropriate in this analysis if there is a linear relationship between the two variables or a line of best fit. This will facilitate the predictive capabilities of the model. In such an instance, the scatterplot will have clusters of size and price points populating the graph in a particular direction (positive or negative). It will clearly show the predictor and response variables. A predictor or independent variable is a factor in the relationship that can predict the value of another (the response or dependent variable). For this investigation, the predictor variable will be square footage and the response variable will be listing price.

*Random sample of 50 properties*

Region | State | County | listing price | $’s/ sqft | sqft |

South Atlantic | NC | Edgecombe | 349,400 | $170 | 2,061 |

West South Central | TX | Coryell | 184,100 | $126 | 1,460 |

Pacific | CA | Contra costa | 366,500 | $225 | 1,626 |

New England | VT | Windsor | 731,000 | $137 | 5,319 |

Mid Atlantic | MD | Baltimore city | 351,000 | $189 | 1,861 |

East South Central | AL | Baldwin | 197,100 | $120 | 1,646 |

New England | CT | Windham | 381,900 | $154 | 2,475 |

New England | ME | Penobscot | 307,400 | $177 | 1,740 |

Mountain | CO | Weld | 382,600 | $178 | 2,151 |

Northeast | PA | Erie | 229,200 | $181 | 1,263 |

Pacific | WA | Clark | 460,700 | $240 | 1,922 |

Pacific | CA | Napa | 404,100 | $228 | 1,769 |

Mountain | MT | Yellowstone | 326,000 | $198 | 1,643 |

East North Central | IL | Peoria | 187,900 | $131 | 1,434 |

Pacific | HI | Honolulu | 273,300 | $224 | 1,220 |

Northeast | NY | Saratoga | 304,600 | $157 | 1,946 |

South Atlantic | FL | Bay | 309,700 | $169 | 1,830 |

New England | MA | Essex | 391,300 | $179 | 2,183 |

East South Central | TN | McMinn | 234,900 | $108 | 2,176 |

Pacific | WA | Kitsap | 362,900 | $249 | 1,459 |

Northeast | NY | Oneida | 308,500 | $168 | 1,840 |

West South Central | LA | East baton rouge | 254,100 | $135 | 1,881 |

Northeast | NY | Wayne | 321,300 | $204 | 1,573 |

Mountain | MT | Cascade | 296,000 | $126 | 2,341 |

Mid Atlantic | VA | Rockingham | 313,400 | $210 | 1,490 |

Pacific | CA | Marin | 420,800 | $227 | 1,856 |

East North Central | IN | Vanderburgh | 214,100 | $134 | 1,596 |

Mid Atlantic | MD | Worcester | 274,400 | $226 | 1,215 |

West South Central | OK | Carter | 263,000 | $142 | 1,856 |

South Atlantic | GA | Paulding | 348,200 | $154 | 2,263 |

West North Central | MN | Sherburne | 361,600 | $177 | 2,041 |

East South Central | KY | Daviess | 239,800 | $113 | 2,118 |

Northeast | NY | Schenectady | 331,300 | $163 | 2,031 |

Mountain | MT | Lewis and Clark | 287,300 | $187 | 1,533 |

West North Central | ND | Grand forks | 394,400 | $169 | 2,338 |

West South Central | OK | Washington | 167,100 | $110 | 1,526 |

Northeast | PA | Lancaster | 248,500 | $170 | 1,465 |

West South Central | AR | Faulkner | 280,500 | $129 | 2,168 |

West South Central | TX | Nacogdoches | 630,800 | $124 | 5,107 |

Mountain | WY | Laramie | 292,500 | $202 | 1,448 |

East North Central | MI | Lenawee | 191,500 | $118 | 1,628 |

South Atlantic | SC | Orangeburg | 305,400 | $172 | 1,780 |

East North Central | MI | Shiawassee | 192,400 | $129 | 1,494 |

South Atlantic | SC | Georgetown | 371,300 | $185 | 2,006 |

Pacific | CA | Placer | 314,600 | $266 | 1,182 |

New England | MA | Plymouth | 311,000 | $183 | 1,703 |

Mountain | NV | Washoe | 357,500 | $153 | 2,336 |

Northeast | NY | Livingston | 353,400 | $220 | 1,603 |

West North Central | MN | Chisago | 309,900 | $196 | 1,583 |

Pacific | CA | Solano | 343,700 | $277 | 1,240 |

The sample data above draws from the list of 100 properties sold in the US in 2019. The analyst used the random function of MS Excel to shuffle the list and picked the first 50 houses listed as the sample for this analysis. As instructed at the start of the process, he chose the size in square feet as the predictor variable and the listing price as the response variable.

*Histograms*

For property size the shape of the graph is skewed right or positively skewed because there are many properties listed in the lower end of property size listing. The center of the graph which is the mean is therefore in the first bin or size category (1182 – 2182) because it is 1908.5 sqft. The spread which is the standard deviation is 757.2 sqft. There are two outliers in the 4182 – 5182 (5107 sqft) category and the 5182 – 6182 (5319). There is also a gap in the 3182 – 4182 where there is no listing

For listing price, the shape of the graph is bell shaped or normally distributed because there are many properties listed in the central category of 267,100 – 367,100. The center of the graph which is the mean is therefore in the second bin or listing price category (267,100 – 367,100) because it is $320,678. The spread which is the standard deviation is $100761.1. There are two outliers in the 567,100 – 667,100 ($630,800) category and the 667,100 – 767,100 (731,000). There is also a gap in the 467,100 – 567,100 category where there is no listing

*Summary sample statistics*

square feet | listing price | |

Mean | 1908.5 | 320678.0 |

Median | 1774.5 | 310450.0 |

Standard Deviation | 757.2 | 100761.1 |

*Summary national statistics*

Square feet | Listing price ($) | |

Mean | 2,111 | 342,365 |

Median | 1,881 | 318,000 |

Std. Dev. | 921 | 125,914 |

The summary sample statistics are lower than the summary national statistics in every category as observable in the tables above. Hence the sample is not representative of the national market statistics.

A regression model can be developed for the data as observable in the scatter plot above by that regresses listing price ($) against size (sqft).

From the scatterplot the association between size and price is positive, which means an increase in property size leads to an increase in listing price. The R^{2} value is at 0.6183 which means that size can predict upto 61.83% of property listing price i.e. a strong relationship.

The r value is therefore the square root of R^{2} which comes to 0.7863. This is the correlation coefficient, which indicates whether the relationship is positive or negative and how strong it is. A correlation coefficient ranges from -1 to +1 with values closest to the limits indicating strong correlation. The R-value of 0.7863 confirms that the relationship between the two is strong and positive.

*Regression equation*

y = 104.63x + 120996

The slope of the equation is 104.63 which means that for every unit increase in property size there is a 104.63 units increase in listing price. The intercept of the equation is 120,996 which means that before any property is built the average value of the land in the sample should be $120,996

The R^{2} value is at 0.6183 which means that size can predict upto 61.83% of property listing price i.e. a strong relationship.

For example, a property with a size of 2,061 sqft should cost

y = 104.63(2,061) + 120996 = $336638.43

The results above such a property (2061 sqft) is actually present in the sample in South Atlantic region, North Carolina state, Edgecombe county and goes for $349,400. This slight difference shows the accuracy of the equation and also accommodates local factors such as location, property taxes, etc. Accommodating such local factors in a set of national property listings could actually contribute to the increased accuracy of the equation, which would make predictions more focused. One question that could be interesting for follow-up research is therefore, what factors apart from property size and can accurately predict the property listing price in the US real estate market.

**References**

Flaxman, S. (2018). Predictor Variable Prioritization in Nonlinear Models with RATE.

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