Homes sold recently in Springfield Home 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 Price $571,500 $571,000 $574,000 $473,500 $599,000 $573,000 $758,000 $753,500 $596,000 $520,000 $662,500 $615,000 $513,000 $631,500 $884,000 $729,000 $735,500 $418,000 $557,000 $836,000 $581,000 $569,000 $458,500 $530,500 $782,000 $746,500 $685,000 $496,500 $345,500 $940,000 $910,000 $561,500 $675,000 $698,000 $589,000 $585,500 $587,500 $735,000 $656,500 $541,000 $533,000 $668,000 $528,000 $770,000 $832,500 $516,000 SqFt 1790 2030 1740 1980 2130 1780 1830 2160 2110 1730 2030 1870 1910 2150 2590 1780 2190 1990 1700 1920 1790 2000 1690 1820 2210 2290 2000 1700 1600 2040 2250 1930 2250 2280 2000 2080 1880 2420 1720 1740 1560 1840 1990 1920 1940 1810 Bedrooms Bathrooms 2 2 4 2 3 2 3 2 3 3 3 2 3 3 4 2 4 2 3 3 3 2 2 2 3 2 3 3 4 3 4 2 3 3 3 3 2 2 3 3 3 2 3 2 3 2 3 2 4 3 4 3 4 2 3 2 2 2 4 3 4 3 2 2 3 3 5 3 2 2 3 3 2 2 4 3 3 2 3 2 2 2 4 3 2 2 3 2 3 3 3 2 Offers 2 3 1 3 3 2 3 2 3 3 3 2 4 5 4 1 4 4 1 2 3 4 3 3 2 3 3 2 3 1 3 2 3 4 3 3 2 4 1 2 1 2 3 1 2 3 Brick No No No No No No Yes No No No Yes Yes No Yes No No Yes No Yes Yes No No No Yes Yes No No No No Yes Yes Yes Yes Yes No No No No No No No No No Yes Yes No Neighborhood North North North North North West East East North North North North West West East East North West North East North West West West North West East North West East East West North North West West West East East West North East North North East North 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 $649,000 $451,500 $579,500 $537,500 $755,500 $455,500 $587,000 $654,000 $406,500 $628,500 $704,500 $761,500 $690,500 $777,000 $904,500 $504,500 $806,500 $602,500 $651,500 $555,500 $631,000 $759,500 $468,000 $828,000 $833,500 $788,000 $536,500 $628,500 $721,000 $534,500 $649,000 $882,500 $606,500 $718,000 $717,000 $921,500 $824,000 $738,500 $452,500 $941,500 $513,500 $862,500 $638,500 $489,000 $715,500 $582,500 $713,000 $785,500 $803,000 1990 2050 1980 1700 2100 1860 2150 2100 1650 1720 2190 2240 1840 2090 2200 1610 2220 1910 1860 1450 2210 2040 2140 2080 1950 2160 1650 2040 2140 1900 1930 2280 2130 1780 2190 2140 2050 2410 1520 2250 1900 1880 1930 2010 1920 2150 2110 2080 2150 2 3 2 3 3 2 2 3 3 2 3 4 3 4 3 2 4 2 3 2 3 4 3 4 3 4 3 3 3 2 3 4 3 4 3 4 2 3 2 4 4 3 3 2 4 3 3 3 4 3 2 2 2 2 2 3 2 2 2 2 3 3 2 3 2 3 3 2 2 3 3 2 3 3 2 2 3 3 2 2 3 2 2 3 3 2 3 2 3 2 3 3 2 2 2 2 3 3 2 6 2 3 3 3 4 3 3 2 3 3 1 1 1 2 2 2 2 1 4 3 4 3 3 1 3 2 3 2 2 3 3 1 4 2 1 2 3 2 4 1 2 4 2 2 2 2 3 No No No Yes Yes No No No No Yes Yes No No No No No No No No Yes No No No No Yes No No No No No No Yes No No Yes Yes Yes No No Yes No Yes No No No No No No Yes West West North West North West West West West North North East East East East West East North East West West North West East East East West North East West East East West East North East East North West East West East West West East North East North East 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 $762,500 $666,500 $634,000 $727,500 $855,000 $516,000 $615,500 $684,000 $1,056,000 $411,500 $734,500 $542,500 $670,000 $585,000 $543,500 $558,000 $574,500 $618,000 $578,500 $622,500 $512,500 $997,500 $589,000 $751,000 $548,500 $552,000 $528,000 $724,000 $598,500 $739,500 $567,500 $749,500 $623,000 1970 2440 2000 2060 2080 2010 2260 2410 2440 1910 2530 2130 1890 1990 2110 1710 1740 1940 2000 2010 1900 2290 1920 1950 1920 1930 1930 2060 1900 2160 2070 2020 2250 2 3 2 3 3 3 3 3 4 3 4 3 3 3 3 2 2 2 3 4 3 5 3 3 2 2 3 2 3 4 2 3 3 2 3 2 2 3 2 3 3 3 2 3 2 2 3 2 2 2 2 2 3 3 4 2 2 2 3 3 2 3 3 2 3 3 1 3 1 1 2 5 5 4 3 4 4 4 1 3 3 1 2 2 3 2 3 1 2 3 4 3 3 1 3 3 2 1 4 Yes No Yes No Yes No No No Yes No No No Yes Yes No No No Yes Yes No No Yes No Yes No No No Yes Yes Yes No No No East North North East East West North North East North East West North North North West West North West North West East West West West West North North North North West East West Deliverable Instructions Your submission should consist of only those exhibits that are specifically asked for. Please ensure that each exhibit is well edited and appropriately formatted. Problem This assignment is an analysis of house prices in Springfield. You will find data in the file House Prices (Excel file) (Links to an external site.) on 128 recent sales of single-family houses in Springfield has the following variables: Price: Price at which house was eventually sold SqFt: Floor area in square feet Bedrooms: Number of bedrooms Bathrooms: Number of bathrooms Offers: Number of offers made on the house prior to the accepted offer Brick: Whether the construction is primarily brick or not (yes or no) Neighborhood: One of the three neighborhoods in Springfield (east, west or north) Use StatTools to conduct the statistical analysis asked below. For questions that ask for a price (or change in price), use zero decimal places in your final numerical answer. Part A - Linear Regression Create a regression model for Price using SqFt, Bedrooms, Bathrooms and Offers as the independent (explanatory) variables. Let us call this Model A. Include the StatTools regression output as Exhibit A. 1. Write out the estimated regression equation. 2. The coefficient of SqFt is 309.20. Provide an economic interpretation of this number. 3. Suppose a homeowner adds an extension to her house in the form of a 400 sq ft. bedroom. What is the increase in the predicted selling price of her house? 4. Estimate the price of a 1720 sq ft. house that has 3 bedrooms, 2 bathrooms and has had 1 offer made on it. 5. Consider house number 39 in the data set. It has 1720 sq ft., 3 bedrooms, 2 bathrooms and has had 1 offer made on it. Suppose the list price is $656,500. o According to Model A, is this house over-priced or under-priced? o By how much? Part B - Adding Categorical Variables Create a regression model for Price using the quantitative as well as qualitative (categorical) variables in the spreadsheet. Use \"North\" as the base (or reference) category for the Neighborhood variable, and \"No Brick\" as the base category for exterior construction material variable, Brick. Let us refer to this model as Model B. Include the StatTools regression output as Exhibit B. 1. According to Model B estimated above, by how much does average price in the East exceed the average price of a similar house in the North? 2. According to Model B, by how much does the average price in the West exceed the average price of a similar house in the East? 3. Let us define the \"brick premium\" as the average amount by which the price of a brick house exceeds the price of a similar house made without brick. According to Model B, what is the brick premium in Springfield? Part C - Adding Interactions In Model B the brick premium was defined to be \"the average amount by which the price of a brick house exceeds the price of similar house made without brick.\" Next, suppose it is conjectured that the brick premium varies by neighborhood. To account for this conjecture, we augment Model B with interaction terms as follows: Price = a + b1SqFt + b2Bedrooms + b3Bathrooms + b4Offers + b5BrickYes + b6East + b7West + b8BrickYes*East + b9BrickYes*West Let us call this model Model C. 1. Simplify the equation for Model C for the various segments as asked below. In this part, we are looking for algebraic answers, not numerical answers. For simplicity, let S = a + b1SqFt + b2Bedrooms + b3Bathrooms + b4Offers. o What is the price of a non-Brick house in the North? o What is the price of a Brick house in the North? o What is the brick premium in the North o What is the price of a non-Brick house in the East? o What is the price of a Brick house in the East? o What is the brick premium in the East? o What is the price of a non-Brick house in the West? o What is the price of a Brick house in the West? o What is the brick premium in the West? 2. Provide an economic interpretation of b8. 3. Provide an economic interpretation of b9. 4. Run Model C using StatTools. Include the regression output as Exhibit C. 5. Use this output, what is the brick premium in the North, East and West? Part D - Nonlinear Regression Run the following regression as Model D: Log(Price) = a + b1SqFt + b2Bedrooms + b3Bathrooms + b4Offers + b5BrickYes + b6East + b7West Recall that for our purposes, \"Log\" refers to natural logarithms. 1. Include the StatTools output as Exhibit D. 2. Estimate the price of a 1720 sq ft. brick house in the North that has 3 bedrooms, 2 bathrooms and has had 1 offer made on it. 3. From the output, it is seen that b7 = _______________. Provide an economic interpretation. 4. Suppose a homeowner adds an extension to her house in the form of a 400 sq ft. bedroom. According to Model D, what is the increase in the predicted selling price of her house? StatTools Report Analysis: Regression Performed By: Date: Monday, March 06, 2017 Updating: Static Variable: Price Multiple Regression for Price Summary ANOVA Table Explained Unexplained Multiple_x000D_ R R-Square Adjusted_x000D_ R-square Std. Err. of_x000D_ Estimate Rows_x000D_ Ignored 0.9320 0.8686 0.8610 50094.720932 0 Degrees of_x000D_ Freedom Sum of_x000D_ Squares Mean of_x000D_ Squares F p-Value 7 120 Standard_x000D_ Error t-Value 97284.238574 264.96870405 21233.969458 39416.392465 -41337.441592 -86486.747638 103405.18675 -7802.8955973 45372.906063 28.671200978 7989.5542373 10585.177031 5423.8839969 9908.0818562 15744.768961 11983.82711 2.1441042026 9.2416325445 2.6577164167 3.7237348369 -7.6213727313 -8.7289092775 6.567589973 -0.6511188392 Brick Neighborhood No No No Yes Yes Yes East North West East North West Coefficient Regression Table Constant SqFt Bedrooms Bathrooms Offers Brick (No) Neighborhood (East) Neighborhood (North) Regression Equation 1.99099E+012 284427518514 113.3411694 301137727827 2509481065.2 p-Value < 0.0001 Confidence Interval 95% Lower 0.0340 < 0.0001 0.0089 0.0003 < 0.0001 < 0.0001 < 0.0001 0.5162 7449.042293 208.20172148 5415.2081008 18458.478618 -52076.354431 -106104.06016 72231.639967 -31530.039261 Price = 114202.67769003 + 264.96870405 SqFt + 21233.96945825 Be Price = 2994.59533935 + 264.96870405 SqFt + 21233.96945825 Bedr Price = 10797.49093661 + 264.96870405 SqFt + 21233.96945825 Bed Price = 200689.42532761 + 264.96870405 SqFt + 21233.96945825 Be Price = 89481.34297692 + 264.96870405 SqFt + 21233.96945825 Bed Price = 97284.23857418 + 264.96870405 SqFt + 21233.96945825 Bed Outliers 0 Confidence Interval 95% Upper 187119.43486 321.73568662 37052.730816 60374.306311 -30598.528752 -66869.435114 134578.73354 15924.248067 870405 SqFt + 21233.96945825 Bedrooms + 39416.39246464 Bathrooms - 41337.44159153 Offers 0405 SqFt + 21233.96945825 Bedrooms + 39416.39246464 Bathrooms - 41337.44159153 Offers 70405 SqFt + 21233.96945825 Bedrooms + 39416.39246464 Bathrooms - 41337.44159153 Offers 870405 SqFt + 21233.96945825 Bedrooms + 39416.39246464 Bathrooms - 41337.44159153 Offers 70405 SqFt + 21233.96945825 Bedrooms + 39416.39246464 Bathrooms - 41337.44159153 Offers 70405 SqFt + 21233.96945825 Bedrooms + 39416.39246464 Bathrooms - 41337.44159153 Offers StatTools Report Analysis: Regression Performed By: Wicky Date: Monday, March 06, 2017 Updating: Static Variable: Price Multiple Regression for Price Summary ANOVA Table Explained Unexplained Multiple_x000D_ R R-Square Adjusted_x000D_ R-square Std. Err. of_x000D_ Estimate Rows_x000D_ Ignored 0.8356 0.6982 0.6884 74996.227575 0 Degrees of_x000D_ Freedom Sum of_x000D_ Squares Mean of_x000D_ Squares F p-Value 4 123 Coefficient Regression Table Constant SqFt Bedrooms Bathrooms Offers -86736.884743 309.1997305 46598.76301 63231.737432 -68005.057061 1.60032E+012 400081239227 71.132709268 691805400516 5624434150.5 Standard_x000D_ Error t-Value 63624.481528 41.318869215 10743.772201 15548.310143 6624.0932927 -1.3632627357 7.4832573199 4.3372813699 4.0667916224 -10.266319337 p-Value < 0.0001 Confidence Interval 95% Lower 0.1753 < 0.0001 < 0.0001 < 0.0001 < 0.0001 -212677.6448 227.41156235 25332.124692 32454.810847 -81117.043579 Regression Equation Price = - 86736.88474264 + 309.1997305 SqFt + 46598.76301031 Bedrooms + 63231.737432 Bathroo Outliers 0 Confidence Interval 95% Upper 39203.875313 390.98789865 67865.401329 94008.664017 -54893.070544 edrooms + 63231.737432 Bathrooms - 68005.05706143 Offers StatTools Report Analysis: Regression Performed By: Date: Wednesday, March 08, 2017 Updating: Static Variable: Price Multiple Regression for Price Summary ANOVA Table Explained Unexplained Multiple_x000D_ R R-Square Adjusted_x000D_ R-square Std. Err. of_x000D_ Estimate Rows_x000D_ Ignored 0.9320 0.8686 0.8610 50094.720932 0 Degrees of_x000D_ Freedom Sum of_x000D_ Squares Mean of_x000D_ Squares F p-Value 7 120 Coefficient Regression Table Constant SqFt Bedrooms Bathrooms Offers Brick (No) Neighborhood (East) Neighborhood (North) 97284.238574 264.96870405 21233.969458 39416.392465 -41337.441592 -86486.747638 103405.18675 -7802.8955973 1.99099E+012 284427518514 113.3411694 301137727827 2509481065.2 Standard_x000D_ Error t-Value 45372.906063 28.671200978 7989.5542373 10585.177031 5423.8839969 9908.0818562 15744.768961 11983.82711 2.1441042026 9.2416325445 2.6577164167 3.7237348369 -7.6213727313 -8.7289092775 6.567589973 -0.6511188392 p-Value < 0.0001 Confidence Interval 95% Lower 0.0340 < 0.0001 0.0089 0.0003 < 0.0001 < 0.0001 < 0.0001 0.5162 7449.042293 208.20172148 5415.2081008 18458.478618 -52076.354431 -106104.06016 72231.639967 -31530.039261 Outliers 0 Confidence Interval 95% Upper 187119.43486 321.73568662 37052.730816 60374.306311 -30598.528752 -66869.435114 134578.73354 15924.248067 StatTools Report Analysis: Regression Performed By: Date: Wednesday, March 08, 2017 Updating: Static Variable: log(price) Multiple Regression for log(price) Summary ANOVA Table Explained Unexplained Multiple_x000D_ R R-Square Adjusted_x000D_ R-square Std. Err. of_x000D_ Estimate Rows_x000D_ Ignored 0.9208 0.8478 0.8389 0.0826197572 0 Degrees of_x000D_ Freedom Sum of_x000D_ Squares Mean of_x000D_ Squares F p-Value 7 120 Coefficient Regression Table Constant SqFt Bedrooms Bathrooms Offers Brick (No) Neighborhood (East) Neighborhood (North) 4.5627755912 0.6518250845 95.491175788 0.8191229136 0.0068260243 Standard_x000D_ Error t-Value 12.489776939 0.0748322061 166.90376492 0.0004353623 4.728657E-005 9.2068915138 0.0289042831 0.013176938 2.1935508187 0.0545332369 0.0174578227 3.1237135269 -0.0683870319 0.0089454531 -7.6448929708 -0.1255414621 0.0163411094 -7.6825543891 0.1516093548 0.0259673867 5.838452546 -0.0002446025 0.0197645753 -0.0123758054 p-Value < 0.0001 Confidence Interval 95% Lower < 0.0001 < 0.0001 0.0302 0.0022 < 0.0001 < 0.0001 < 0.0001 0.9901 12.341614379 0.0003417382 0.0028148629 0.0199679629 -0.0860984065 -0.1578957215 0.1001957364 -0.0393770862 Outliers 0 Confidence Interval 95% Upper 12.637939499 0.0005289865 0.0549937033 0.0890985109 -0.0506756572 -0.0931872026 0.2030229733 0.0388878811 StatTools Report Analysis: Regression Performed By: Date: Monday, March 06, 2017 Updating: Static Variable: Price Multiple Regression for Price Summary ANOVA Table Explained Unexplained Multiple_x000D_ R R-Square Adjusted_x000D_ R-square Std. Err. of_x000D_ Estimate Rows_x000D_ Ignored 0.9320 0.8686 0.8610 50094.720932 0 Degrees of_x000D_ Freedom Sum of_x000D_ Squares Mean of_x000D_ Squares F p-Value 7 120 Standard_x000D_ Error t-Value 97284.238574 264.96870405 21233.969458 39416.392465 -41337.441592 -86486.747638 103405.18675 -7802.8955973 45372.906063 28.671200978 7989.5542373 10585.177031 5423.8839969 9908.0818562 15744.768961 11983.82711 2.1441042026 9.2416325445 2.6577164167 3.7237348369 -7.6213727313 -8.7289092775 6.567589973 -0.6511188392 Brick Neighborhood No No No Yes Yes Yes East North West East North West Coefficient Regression Table Constant SqFt Bedrooms Bathrooms Offers Brick (No) Neighborhood (East) Neighborhood (North) Regression Equation 1.99099E+012 284427518514 113.3411694 301137727827 2509481065.2 p-Value < 0.0001 Confidence Interval 95% Lower 0.0340 < 0.0001 0.0089 0.0003 < 0.0001 < 0.0001 < 0.0001 0.5162 7449.042293 208.20172148 5415.2081008 18458.478618 -52076.354431 -106104.06016 72231.639967 -31530.039261 Price = 114202.67769003 + 264.96870405 SqFt + 21233.96945825 Be Price = 2994.59533935 + 264.96870405 SqFt + 21233.96945825 Bedr Price = 10797.49093661 + 264.96870405 SqFt + 21233.96945825 Bed Price = 200689.42532761 + 264.96870405 SqFt + 21233.96945825 Be Price = 89481.34297692 + 264.96870405 SqFt + 21233.96945825 Bed Price = 97284.23857418 + 264.96870405 SqFt + 21233.96945825 Bed Outliers 0 Confidence Interval 95% Upper 187119.43486 321.73568662 37052.730816 60374.306311 -30598.528752 -66869.435114 134578.73354 15924.248067 870405 SqFt + 21233.96945825 Bedrooms + 39416.39246464 Bathrooms - 41337.44159153 Offers 0405 SqFt + 21233.96945825 Bedrooms + 39416.39246464 Bathrooms - 41337.44159153 Offers 70405 SqFt + 21233.96945825 Bedrooms + 39416.39246464 Bathrooms - 41337.44159153 Offers 870405 SqFt + 21233.96945825 Bedrooms + 39416.39246464 Bathrooms - 41337.44159153 Offers 70405 SqFt + 21233.96945825 Bedrooms + 39416.39246464 Bathrooms - 41337.44159153 Offers 70405 SqFt + 21233.96945825 Bedrooms + 39416.39246464 Bathrooms - 41337.44159153 Offers StatTools Report Analysis: Regression Performed By: Wicky Date: Monday, March 06, 2017 Updating: Static Variable: Price Multiple Regression for Price Summary ANOVA Table Explained Unexplained Multiple_x000D_ R R-Square Adjusted_x000D_ R-square Std. Err. of_x000D_ Estimate Rows_x000D_ Ignored 0.8356 0.6982 0.6884 74996.227575 0 Degrees of_x000D_ Freedom Sum of_x000D_ Squares Mean of_x000D_ Squares F p-Value 4 123 Coefficient Regression Table Constant SqFt Bedrooms Bathrooms Offers -86736.884743 309.1997305 46598.76301 63231.737432 -68005.057061 1.60032E+012 400081239227 71.132709268 691805400516 5624434150.5 Standard_x000D_ Error t-Value 63624.481528 41.318869215 10743.772201 15548.310143 6624.0932927 -1.3632627357 7.4832573199 4.3372813699 4.0667916224 -10.266319337 p-Value < 0.0001 Confidence Interval 95% Lower 0.1753 < 0.0001 < 0.0001 < 0.0001 < 0.0001 -212677.6448 227.41156235 25332.124692 32454.810847 -81117.043579 Regression Equation Price = - 86736.88474264 + 309.1997305 SqFt + 46598.76301031 Bedrooms + 63231.737432 Bathroo Outliers 0 Confidence Interval 95% Upper 39203.875313 390.98789865 67865.401329 94008.664017 -54893.070544 edrooms + 63231.737432 Bathrooms - 68005.05706143 Offers StatTools Report Analysis: Regression Performed By: Date: Wednesday, March 08, 2017 Updating: Static Variable: Price Multiple Regression for Price Summary ANOVA Table Explained Unexplained Multiple_x000D_ R R-Square Adjusted_x000D_ R-square Std. Err. of_x000D_ Estimate Rows_x000D_ Ignored 0.9320 0.8686 0.8610 50094.720932 0 Degrees of_x000D_ Freedom Sum of_x000D_ Squares Mean of_x000D_ Squares F p-Value 7 120 Coefficient Regression Table Constant SqFt Bedrooms Bathrooms Offers Brick (No) Neighborhood (East) Neighborhood (North) 97284.238574 264.96870405 21233.969458 39416.392465 -41337.441592 -86486.747638 103405.18675 -7802.8955973 1.99099E+012 284427518514 113.3411694 301137727827 2509481065.2 Standard_x000D_ Error t-Value 45372.906063 28.671200978 7989.5542373 10585.177031 5423.8839969 9908.0818562 15744.768961 11983.82711 2.1441042026 9.2416325445 2.6577164167 3.7237348369 -7.6213727313 -8.7289092775 6.567589973 -0.6511188392 p-Value < 0.0001 Confidence Interval 95% Lower 0.0340 < 0.0001 0.0089 0.0003 < 0.0001 < 0.0001 < 0.0001 0.5162 7449.042293 208.20172148 5415.2081008 18458.478618 -52076.354431 -106104.06016 72231.639967 -31530.039261 Outliers 0 Confidence Interval 95% Upper 187119.43486 321.73568662 37052.730816 60374.306311 -30598.528752 -66869.435114 134578.73354 15924.248067 StatTools Report Analysis: Regression Performed By: Date: Wednesday, March 08, 2017 Updating: Static Variable: log(price) Multiple Regression for log(price) Summary ANOVA Table Explained Unexplained Multiple_x000D_ R R-Square Adjusted_x000D_ R-square Std. Err. of_x000D_ Estimate Rows_x000D_ Ignored 0.9208 0.8478 0.8389 0.0826197572 0 Degrees of_x000D_ Freedom Sum of_x000D_ Squares Mean of_x000D_ Squares F p-Value 7 120 Coefficient Regression Table Constant SqFt Bedrooms Bathrooms Offers Brick (No) Neighborhood (East) Neighborhood (North) 4.5627755912 0.6518250845 95.491175788 0.8191229136 0.0068260243 Standard_x000D_ Error t-Value 12.489776939 0.0748322061 166.90376492 0.0004353623 4.728657E-005 9.2068915138 0.0289042831 0.013176938 2.1935508187 0.0545332369 0.0174578227 3.1237135269 -0.0683870319 0.0089454531 -7.6448929708 -0.1255414621 0.0163411094 -7.6825543891 0.1516093548 0.0259673867 5.838452546 -0.0002446025 0.0197645753 -0.0123758054 p-Value < 0.0001 Confidence Interval 95% Lower < 0.0001 < 0.0001 0.0302 0.0022 < 0.0001 < 0.0001 < 0.0001 0.9901 12.341614379 0.0003417382 0.0028148629 0.0199679629 -0.0860984065 -0.1578957215 0.1001957364 -0.0393770862 Outliers 0 Confidence Interval 95% Upper 12.637939499 0.0005289865 0.0549937033 0.0890985109 -0.0506756572 -0.0931872026 0.2030229733 0.0388878811