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Building regression models for finding house prices

Assignment Help Business Management
Reference no: EM133047960

Assignment:

  • This is an individual assignment.
  • Submit one Word/PDF file with your answers for all questions and one Excel file to show your regression models.
  • Attach StatTools reports (including the user's name and creation date) that are specifically asked for in your Word or PDF document.

In this assignment we will build regression models to analyze the house prices in Springfield. The file House Prices (Excel) (Links to an external site.) contains 128 recent sales of single-family houses in Springfield with the following variables:

Homes sold recently in Springfield

Home

Price

SqFt

Bedrooms

Bathrooms

Offers

Brick

Neighborhood

1

$571,500

1790

2

2

2

No

North

2

$571,000

2030

4

2

3

No

North

3

$574,000

1740

3

2

1

No

North

4

$473,500

1980

3

2

3

No

North

5

$599,000

2130

3

3

3

No

North

6

$573,000

1780

3

2

2

No

West

7

$758,000

1830

3

3

3

Yes

East

8

$753,500

2160

4

2

2

No

East

9

$596,000

2110

4

2

3

No

North

10

$520,000

1730

3

3

3

No

North

11

$662,500

2030

3

2

3

Yes

North

12

$615,000

1870

2

2

2

Yes

North

13

$513,000

1910

3

2

4

No

West

14

$631,500

2150

3

3

5

Yes

West

15

$884,000

2590

4

3

4

No

East

16

$729,000

1780

4

2

1

No

East

17

$735,500

2190

3

3

4

Yes

North

18

$418,000

1990

3

3

4

No

West

19

$557,000

1700

2

2

1

Yes

North

20

$836,000

1920

3

3

2

Yes

East

21

$581,000

1790

3

2

3

No

North

22

$569,000

2000

3

2

4

No

West

23

$458,500

1690

3

2

3

No

West

24

$530,500

1820

3

2

3

Yes

West

25

$782,000

2210

4

3

2

Yes

North

26

$746,500

2290

4

3

3

No

West

27

$685,000

2000

4

2

3

No

East

28

$496,500

1700

3

2

2

No

North

29

$345,500

1600

2

2

3

No

West

30

$940,000

2040

4

3

1

Yes

East

31

$910,000

2250

4

3

3

Yes

East

32

$561,500

1930

2

2

2

Yes

West

33

$675,000

2250

3

3

3

Yes

North

34

$698,000

2280

5

3

4

Yes

North

35

$589,000

2000

2

2

3

No

West

36

$585,500

2080

3

3

3

No

West

37

$587,500

1880

2

2

2

No

West

38

$735,000

2420

4

3

4

No

East

39

$656,500

1720

3

2

1

No

East

40

$541,000

1740

3

2

2

No

West

41

$533,000

1560

2

2

1

No

North

42

$668,000

1840

4

3

2

No

East

43

$528,000

1990

2

2

3

No

North

44

$770,000

1920

3

2

1

Yes

North

45

$832,500

1940

3

3

2

Yes

East

46

$516,000

1810

3

2

3

No

North

47

$649,000

1990

2

3

2

No

West

48

$451,500

2050

3

2

6

No

West

49

$579,500

1980

2

2

2

No

North

50

$537,500

1700

3

2

3

Yes

West

51

$755,500

2100

3

2

3

Yes

North

52

$455,500

1860

2

2

3

No

West

53

$587,000

2150

2

3

4

No

West

54

$654,000

2100

3

2

3

No

West

55

$406,500

1650

3

2

3

No

West

56

$628,500

1720

2

2

2

Yes

North

57

$704,500

2190

3

2

3

Yes

North

58

$761,500

2240

4

3

3

No

East

59

$690,500

1840

3

3

1

No

East

60

$777,000

2090

4

2

1

No

East

61

$904,500

2200

3

3

1

No

East

62

$504,500

1610

2

2

2

No

West

63

$806,500

2220

4

3

2

No

East

64

$602,500

1910

2

3

2

No

North

65

$651,500

1860

3

2

2

No

East

66

$555,500

1450

2

2

1

Yes

West

67

$631,000

2210

3

3

4

No

West

68

$759,500

2040

4

3

3

No

North

69

$468,000

2140

3

2

4

No

West

70

$828,000

2080

4

3

3

No

East

71

$833,500

1950

3

3

3

Yes

East

72

$788,000

2160

4

2

1

No

East

73

$536,500

1650

3

2

3

No

West

74

$628,500

2040

3

3

2

No

North

75

$721,000

2140

3

3

3

No

East

76

$534,500

1900

2

2

2

No

West

77

$649,000

1930

3

2

2

No

East

78

$882,500

2280

4

3

3

Yes

East

79

$606,500

2130

3

2

3

No

West

80

$718,000

1780

4

2

1

No

East

81

$717,000

2190

3

3

4

Yes

North

82

$921,500

2140

4

3

2

Yes

East

83

$824,000

2050

2

2

1

Yes

East

84

$738,500

2410

3

3

2

No

North

85

$452,500

1520

2

2

3

No

West

86

$941,500

2250

4

3

2

Yes

East

87

$513,500

1900

4

2

4

No

West

88

$862,500

1880

3

3

1

Yes

East

89

$638,500

1930

3

3

2

No

West

90

$489,000

2010

2

2

4

No

West

91

$715,500

1920

4

2

2

No

East

92

$582,500

2150

3

2

2

No

North

93

$713,000

2110

3

2

2

No

East

94

$785,500

2080

3

3

2

No

North

95

$803,000

2150

4

3

3

Yes

East

96

$762,500

1970

2

2

1

Yes

East

97

$666,500

2440

3

3

3

No

North

98

$634,000

2000

2

2

1

Yes

North

99

$727,500

2060

3

2

1

No

East

100

$855,000

2080

3

3

2

Yes

East

101

$516,000

2010

3

2

5

No

West

102

$615,500

2260

3

3

5

No

North

103

$684,000

2410

3

3

4

No

North

104

$1,056,000

2440

4

3

3

Yes

East

105

$411,500

1910

3

2

4

No

North

106

$734,500

2530

4

3

4

No

East

107

$542,500

2130

3

2

4

No

West

108

$670,000

1890

3

2

1

Yes

North

109

$585,000

1990

3

3

3

Yes

North

110

$543,500

2110

3

2

3

No

North

111

$558,000

1710

2

2

1

No

West

112

$574,500

1740

2

2

2

No

West

113

$618,000

1940

2

2

2

Yes

North

114

$578,500

2000

3

2

3

Yes

West

115

$622,500

2010

4

3

2

No

North

116

$512,500

1900

3

3

3

No

West

117

$997,500

2290

5

4

1

Yes

East

118

$589,000

1920

3

2

2

No

West

119

$751,000

1950

3

2

3

Yes

West

120

$548,500

1920

2

2

4

No

West

121

$552,000

1930

2

3

3

No

West

122

$528,000

1930

3

3

3

No

North

123

$724,000

2060

2

2

1

Yes

North

124

$598,500

1900

3

3

3

Yes

North

125

$739,500

2160

4

3

3

Yes

North

126

$567,500

2070

2

2

2

No

West

127

$749,500

2020

3

3

1

No

East

128

$623,000

2250

3

3

4

No

West

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 variables. Let us call this Model A.

  1. Include the StatTools regression output as Exhibit A. Write out the estimated regression equation (copy and paste the equation from StatTools report).
  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.
    1. According to Model A, is this house over-priced or underpriced?
    2. By how much?

Part B-Adding Categorical Variables

Create a regression model for Price using the numerical as well as categorical variables (Brick and Neighborhood) 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.

  1. Include the StatTools regression output as Exhibit B. Write out the estimated regression equation (copy and paste the equation from StatTools report).
  2. According to Model B estimated above, by how much does the average price in the East exceed the average price of a similar house in the North?
  3. 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?
  4. 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 a 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.
    1. What is the price of a non-Brick house in the North?
    2. What is the price of a Brick house in the North?
    3. What is the price of a non-Brick house in the East?
    4. What is the price of a Brick house in the East?
    5. What is the price of a non-Brick house in the West?
    6. What is the price of a Brick house in the West?
  2. Provide an economic interpretation of b8.
  3. Run Model C using StatTools. Include the regression output as Exhibit C.
  4. 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.

From the output, it is seen that b7 = _______________. Provide an economic interpretation

Reference no: EM133047960

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