# just need some help

*label*Mathematics

*timer*Asked: May 2nd, 2017

*account_balance_wallet*$9.99

### Question Description

i have a couple of questions that need answered pretty soon. there's some regression stuff and some confidence interval things as well.

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## Tutor Answer

Attached.

Regression Analysis and Simulation

Question 1: What Predicts House Prices?

A real estate company wants to know the effect of different house features on house prices. They

collect data on 150 houses (House Prices.xlsx). The variables in the dataset are described in the

first sheet of the excel file.

Run a multiple regression predicting “House Price” with all the other variables in the dataset. Next,

analyze your regression results to answer the following questions:

a)

b)

c)

d)

Write down the regression model/equation.

Show your table of regression results.

By how much is house price expected to change if the house has a lake view?

Is the number of bathrooms a statistically significant predictor of house price? Why or why

not? If yes, what is the difference in predicted house price for a house with 3 bathrooms

versus 2 bathrooms?

e) Is the number of bedrooms a statistically significant predictor of house price? Why or why

not? If yes, what is the effect of an additional bedroom on house price?

f) What is the expected house price for a house with the following features? “house

size”=1,000 sqft, “lot size”=0.5 acres, 4 bedrooms, 3 bathrooms, no lake view, and garage

parking.

g) How much would house price be expected to increase if the house has a parking garage

compared to a house with street parking?

h) According to the regression model, how much of the variation (%) in house prices is

explained by the variation in all the independent variables?

Question 2: TV Hours

Use the following information for the next four questions: the station manager of a local television

station is interested in predicting the amount of television (in hours) that people will watch in the

viewing area. The independent variables are: X1 age (in years), X2 education (highest level

obtained, in years) and X3 family size (number of family members in household). The multiple

regression output is shown below:

Summary measures

Multiple R

R-Square

Adj R-Square

StErr of Estimate

0.8440

0.7123

0.6644

0.5598

Copyright © 2015 by Anita Mukherjee and Hessam Bavafa

Page 1 of 2

a) Use the information above to write the linear regression model

b) What is the relationship between “age” and the amount of television watched?

c) According to the regression model, how much would hours of television watched be

expected to increase if the number of years of education increases by 2?

d) According to the regression model, how much would hours of television watched be

expected to increase if the age of a viewer decreases by 5?

Question 3: McDonald’s Simulation

McDonald’s has built a simulation model of one of its restaurants to measure average customer

wait time.

a) McDonald’s knows that the standard deviation of wait time is around 10min. It wants to

build the 99% confidence interval for the average wait time with ±1 min of error. How

many replications should it run?

b) McDonald’s runs 400 replications. The mean wait time is 5min with a standard deviation

of 9min. What is the 95% confidence interval for customer wait time?

Page 2 of 2

Regression Analysis and Simulation

Question 1: What Predicts House Prices?

A real estate company wants to know the effect of different house features on house prices. They

collect data on 150 houses (House Prices.xlsx). The variables in the dataset are described in the

first sheet of the excel file.

Run a multiple regression predicting “House Price” with all the other variables in the dataset. Next,

analyze your regression results to answer the following questions:

a) Write down the regression model/equation.

b) Show your table of regression results.

SUMMARY OUTPUT

Regression Statistics

Multiple R

0.931741113

R Square

0.868141502

Adjusted R Square

0.862608978

Standard Error

15423.6188

Observations

150

c) By how much is house price expected to change if the house has a lake view?

SUMMARY OUTPUT

Regression Statistics

Multiple R

0.404745579

R Square

0.163818984

Adjusted R Square

0.158169112

Standard Error

38178.5591

Observations

150

Out of 150 total observations, house prices are expected to change if the house has a lake

view by 16% for every $38,178.55 incremental house price increase.

d) Is the number of bathrooms a statistically significant predictor of house price? Why or why

not? If yes, what is the difference in predicted house price for a house with 3 bathrooms

versus 2 bathrooms?

SUMMARY OUTPUT

Regression Statistics

Multiple R

0.660459721

R Square

0.436207043

Adjusted R Square

0.432397631

Standard Error

31349.39797

Observations

150

Yes, the number of bathrooms is a statistically significant predictor of house price because the

value of lit size increase which increase the overall price of the house’s value. The increase in

needed space increases price values.

e) Is the number of bedrooms a statistically significant predictor of house price? Why or why

not? If yes, what is the effect of an additional bedroom on house price?

SUMMARY OUTPUT

Regression Statistics

Multiple R

0.576506309

R Square

0.332359524

Adjusted R Square

0.32784844

Standard Error

34114.63358

Observations

150

Yes, as concept applies as above in which the number of bedrooms a statistically significant

predictor of house price because the value of lit size increase which increase the overall price of

the house’s value. The increase in needed space increases price values.

f)

What is the expected house price for a house with the following features? “house

size”=1,000 sqft, “lot size”=0.5 acres, 4 bedrooms, 3 bathrooms, no lake view, and garage

parking.

SUMMARY OUTPUT

Regression Statistics

Multiple R

0.576506309

R Square

0.332359524

Adjusted R Square

0.32784844

Standard Error

34114.63358

Observations

150

The expected house price for a house with the following features. “House size”=1,000 sqft, “lot

size”=0.5 acres, 4 bedrooms, 3 bathrooms, no lake view, and garage parking is $129,500. See excel

workbook, worksheet title “Data.”

g) How much would house price be expected to increase if the house has a parking garage

compared to a house with street parking?

SUMMARY OUTPUT

Regression Statistics

Multiple R

R Square

Adjusted R Square

Standard Error

Observations

0.165624288

0.027431405

0.020859995

41174.61081

150

House prices are expected to increase if the house has a parking garage compared to a house

with street parking by 16% for every $41,174.61 house pricing increase.

h) According to the regression model, how much of the variation (%) in house prices is

explained by the variation in all the independent variables?

SUMMARY OUTPUT

Regression Statistics

Multiple R

0.931741113

R Square

0.868141502

Adjusted R Square

0.862608978

Standard Error

15423.6188

Observations

150

House pricing will vary depending on specific property needs which dictates the total amount of

footage required, and added amenities. The price value for all variations ranges from 86% to 93%

increase in pricing. Low value prices represent minimal amenities and footage, while higher percentile

ranges represent increased amenities and amount of needed footage.

Question 2: TV Hours

Use the following information for the next four questions: the station manager of a local television

station is interested in predicting the amount of television (in hours) that people will watch in the

viewing area. The independent variables are: X1 age (in years), X2 education (highest level

obtained, in years) and X3 family size (number of family members in household). The multiple

regression output is shown below:

Summary measures

Multiple R

R-Square

Adj R-Square

StErr of Estimate

0.8440

0.7123

0.6644

0.5598

Copyright © 2015 by Anita Mukherjee and Hessam Bavafa

a) Use the information above to write the linear regression model

Page 1 of 2

0.35

0.3

0.25

0.2135

0.2

0.15

0.1

0.0222

0.05

0

-0.05

0.06116

0.0405

0

0.0005

-0.0498

1

0.5

1.5

2

2.5

3

3.5

4

-0.1

-0.15

Independent Variables

Dependent Variables

b) What is the relationship between “age” and the amount of television watched?

The relationship between “age” and the amount of television watched expands between ages

one and three with two years of age watching television majority of the time.

c) According to the regression model, how much would hours of television watched be expected

to increase if the number of years of education increases by two?

0.7

0.6

0.427

0.5

0.4

0.3

0.2

0.1

0.001

0

0.0222

-0.0498

-0.1 0

1

2

0.06116

0.0405

3

4

5

6

-0.2

-0.3

Independent Variables

Dependent Variables

Linear (Independent Variables )

Linear (Dependent Variables )

The amount of hours of television watched expected to increase if the number of years of

education increases by two would increase television-viewing times.

d) According to the regression model, how much would hours of television watched be expected

to increase if the age of a viewer decreases by 5?

0.2

0.15

0.1

0.0427

0.05

0.06116

0.0405

0.0222

0.0001

0

0

1

-0.0498

2

3

4

5

6

-0.05

-0.1

Independent Variables

Dependent Variables

Linear (Independent Variables )

Linear (Dependent Variables )

The amount of hours of television watched expected to increase if the number of years of

education decreases by five would decrease the amount of television viewing times.

Question 3: McDonald’s Simulation

McDonald’s has built a simulation model of one of its restaurants to measure average customer

wait time.

a) McDonald’s knows that the standard deviation of wait time is around 10min. It wants to build

the 99% confidence interval for the average wait time with ±1 min of error. How many

replications should it run?

1 − 𝜕 = 0.99 = 𝜕 = 0.001

𝑠

𝐸 = 𝑡𝜕 ∗ (𝑛 − 1) ∗ (

=

√𝑛)

2

1

𝐸 = 𝑡1 ∗ (10 − 1) ∗ (

= 0.45

2

√10)

b) McDonald’s will need to run one replication ever .45 seconds for 10 minutes equaling 27

replications.

McDonald’s runs 400 replications. The mean wait time is 5min with a standard deviation of

9min. What is the 95% confidence interval for customer wait time?

Variable

Comment

House Price

House Size

Lot Size

Bedrooms

Bathrooms

in dollars

in square feet

in acres

number of bedrooms

number of bathrooms

Yes/No: whether or not house has a

lakeview

Lakeview

Parking Type

"Street Parking", "Driveway Parking",

"Garage Parking"

Hint

You need only one dummy: a variable that is 1 if

the house has lakeview and 0 otherise.

You need only two dummy variables. While you

can include any two of the three categories, we

suggest you create dummies for "Driveway

Parking" and "Street Parking".

Home House Price House Size Lot Size Bedrooms Bathrooms Lakeview Parking Type

1

$102.000

600

0,50

3

1,0

0

2

$146.300

1050

0,43

5

1,5

0

3

$182.000

1800

0,68

7

1,5

1

4

$110.500

922

0,30

5

1,0

0

5

$171.900

1950

0,75

8

2,5

0

6

$154.000

1783

0,22

8

1,5

0

7

$147.000

1008

0,50

6

1,0

1

8

$195.900

1840

1,16

8

2,0

1

9

$183.500

3700

1,10

10

3,0

0

10

$156.500

1092

0,26

6

1,0

1

11

$152.000

1950

0,50

7

1,5

0

12

$170.000

1403

0,50

6

2,0

1

13

$253.000

1680 14,37

8

2,0

0

14

$129.500

1000

0,49

4

1,0

0

15

$241.900

2310

0,46

8

2,5

1

16

$151.900

1300

0,78

6

1,0

1

17

$199.000

1930

3,00

9

3,0

0

18

$186.000

3000

0,50

11

2,5

0

19

$153.500

1362

0,40

7

2,0

0

20

$166.000

1750

0,50

7

2,0

0

21

$224.900

2080

1,00

8

2,5

1

22

$158.500

1344

0,94

6

2,0

0

23

$332.000

2130 11,91

8

1,5

1

24

$172.000

1500

0,41

7

1,0

1

25

$176.000

2400

0,40

7

2,5

0

26

$210.000

2272

0,41

9

2,5

1

27

$156.500

1050

1,00

5

1,0

1

28

$169.500

1610

0,45

8

1,5

1

29

$154.900

1248

0,22

7

1,0

1

30

$163.000

2000

0,50

8

2,0

0

31

$140.000

1450

0,30

6

2,0

0

32

$148.500

1248

0,25

7

1,0

1

33

$224.500

2544

0,28

9

2,5

1

34

$299.900

2500

0,92

8

3,0

1

35

$199.900

2858

0,79

9

3,0

0

36

$220.000

1745

0,58

7

2,5

1

37

$233.000

2653

1,80

9

3,0

1

38

$174.900

1450

0,30

7

1,0

1

39

$124.000

850

0,11

4

1,0

0

40

$169.900

1839

2,60

7

1,5

0

41

$213.000

2016

0,78

8

2,5

1

42

$165.000

1625

0,36

7

1,5

0

43

$162.000

2000

0,11

8

2,0

0

3

2

3

3

1

3

1

3

2

3

2

2

2

3

1

2

3

2

3

3

1

3

1

3

2

3

3

2

3

3

2

2

3

1

2

1

2

3

1

3

3

1

3

44

45

46

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

$211.500

$166.000

$194.000

$192.000

$171.000

$226.800

$155.000

$157.500

$297.000

$315.000

$161.000

$193.500

$163.000

$180.000

$171.000

$163.000

$220.000

$155.900

$219.900

$185.000

$172.500

$167.900

$160.000

$147.000

$210.500

$192.500

$138.000

$200.000

$186.000

$217.000

$180.000

$195.000

$149.000

$165.500

$175.900

$156.000

$235.406

$215.500

$225.000

$155.000

$190.000

$126.000

$172.000

$175.000

2250

1300

1956

2496

1575

1960

1200

1296

1950

2516

1066

2276

1908

1122

3500

1100

2300

1118

2464

2100

1552

1856

1800

1248

2000

1848

1036

2277

2300

2080

1600

2680

1200

1526

1680

1232

2465

2800

2265

1300

1900

864

2000

1800

0,33

0,30

0,50

0,75

0,25

1,33

0,33

0,50

18,70

8,10

0,33

1,00

0,46

3,09

1,00

0,33

5,63

0,56

0,43

0,58

0,46

0,33

0,30

0,30

0,60

0,50

0,95

0,80

0,65

1,23

1,84

0,50

0,25

0,30

0,50

0,31

1,55

1,68

0,85

0,65

1,00

0,32

0,75

0,66

9

7

8

9

7

8

5

9

7

7

5

8

7

5

10

6

7

7

8

8

6

7

7

6

9

7

6

8

7

8

7

9

7

7

6

6

8

9

8

5

8

4

9

8

2,5

1,0

2,5

2,5

1,5

2,5

1,0

1,0

2,5

2,5

1,0

2,5

2,0

2,0

2,5

1,0

2,5

1,5

2,5

1,5

1,5

1,5

1,5

1,0

2,5

2,5

1,0

3,0

3,0

2,5

2,0

3,0

1,0

1,5

1,5

2,0

2,5

1,5

2,5

1,0

2,5

1,0

1,5

2,5

1

1

1

0

1

1

1

1

0

1

1

0

0

1

0

1

0

1

1

1

1

0

0

1

1

1

0

0

0

1

0

0

1

1

1

0

1

1

1

1

0

0

0

0

1

3

2

3

3

1

3

3

3

1

3

3

3

3

2

3

3

2

3

2

3

1

3

2

3

2

1

3

3

3

1

3

3

2

3

1

3

2

3

2

1

1

1

3

88

89

90

91

92

93

94

95

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

129

130

131

$181.500

$180.000

$295.000

$146.000

$165.000

$159.000

$138.500

$194.900

$140.000

$184.000

$164.000

$190.000

$250.000

$156.500

$156.500

$188.000

$202.000

$245.000

$171.900

$119.900

$159.900

$165.000

$165.000

$152.500

$265.000

$164.500

$156.500

$210.000

$157.500

$195.000

$127.000

$130.000

$238.000

$212.000

$205.000

$174.900

$207.000

$261.750

$195.000

$108.000

$209.000

$115.000

$190.000

$171.000

1900

1564

2400

1100

1800

1200

1540

1980

1289

1800

1502

2025

3000

1500

1600

1500

2100

2100

1632

1660

1070

1400

1800

1100

3150

2000

1700

1800

1850

2320

1300

1338

2288

2400

2400

1900

2010

2981

1725

821

3060

875

1760

2000

0,75

0,33

2,00

1,10

1,00

0,33

0,18

0,70

0,25

0,68

0,35

1,10

1,15

0,50

0,26

0,54

1,00

0,50

3,00

0,21

1,69

0,35

0,50

0,37

0,30

0,70

0,30

1,52

0,26

0,40

0,37

0,12

1,20

0,50

0,70

0,44

0,68

1,30

1,53

2,30

0,75

0,26

0,05

0,65

7

6

7

6

8

6

7

8

6

7

7

7

10

7

8

5

8

8

6

7

5

6

7

7

11

8

8

8

9

8

5

6

8

8

8

6

8

10

8

4

8

5

7

7

2,0

2,0

2,0

1,0

2,5

1,0

2,0

2,5

1,0

2,0

1,5

2,0

3,5

1,5

1,5

2,5

2,5

2,5

3,0

1,0

1,0

2,0

2,0

1,0

4,0

1,0

2,0

2,5

2,0

2,5

1,0

1,0

2,5

2,5

3,0

2,0

1,5

3,5

2,5

1,0

2,0

1,0

2,0

1,0

0

1

1

0

0

1

0

0

0

1

1

0

1

0

0

1

1

1

0

0

1

0

0

1

1

0

0

1

0

0

0

0

1

1

0

0

1

1

1

0

0

0

1

0

1

3

1

1

3

3

2

1

1

2

2

1

2

1

1

2

2

1

1

2

3

1

3

3

3

1

3

3

3

1

3

3

1

1

3

1

1

3

2

2

3

3

3

1

132

133

134

135

136

137

138

139

140

141

142

143

144

145

146

147

148

149

150

Min

Mean

Max

Range

STD.

$215.000

$143.500

$220.000

$137.000

$247.000

$224.500

$182.000

$240.000

$170.000

$150.500

$209.900

$182.500

$189.000

$198.500

$128.000

$147.500

$145.000

$305.000

$220.000

$102.000,00

$183.775,04

$332.000,00

$230.000,00

$41.471,96

2600

1624

2473

1100

3100

2300

1450

2100

1650

1600

2790

1786

1728

1900

1165

1300

1080

2820

2100

0,75

1,80

1,25

0,17

0,54

0,91

0,30

0,50

0,50

0,40

0,75

0,30

0,50

1,06

0,12

0,29

0,31

1,00

1,30

8

7

9

5

10

8

6

8

8

6

13

8

8

7

6

6

5

9

8

2,0

1,5

2,5

1,0

3,5

2,5

1,5

2,5

2,5

2,0

2,5

2,0

1,5

2,5

1,0

1,0

1,0

2,5

1,5

1

0

1

0

1

1

1

1

0

0

0

1

1

1

0

1

1

1

1

1=Yes

0=No

3

2

3

1

2

3

3

1

3

3

1

1

3

2

3

1

2

1

1

Garage Parking

Street Parking

Driveway Parking

1

2

3

SUMMARY OUTPUT

Regression Statistics

Multiple R

0,931741113

R Square

0,868141502

Adjusted R Square

0,862608978

Standard Error

15423,6188

Observations

150

ANOVA

df

Regression

Residual

Total

Intercept

House Size

Lot Size

Bedrooms

Bathrooms

Lakeview

Parking Type

6

143

149

SS

2,23971E+11

34017986436

2,57989E+11

MS

37328431975

237888017

Coefficients

91496,34855

30,61732842

7874,740407

-896,5660339

16593,18625

34835,71603

-7165,357871

Standard Error

7392,851826

4,588817929

574,3768045

1518,665589

2818,600879

2548,380495

1481,154858

t Stat

12,37632658

6,672160216

13,71005992

-0,590364357

5,887029403

13,66974677

-4,83768313

RESIDUAL OUTPUT

Observation

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

Predicted House Price

106211,5303

133106,9152

183915,8227

112702,2299

184251,2738

144040,6655

165180,134

196320,4184

239925,8608

151531,3361

159420,6106

186701,8071

267776,6084

117483,1483

227825,5533

169159,9633

194426,4045

Residuals

Standard Residuals

-4211,530336

-0,278726824

13193,08477

0,873142616

-1915,822731

-0,126792672

-2202,229939

-0,145747628

-12351,27376

-0,817430014

9959,334499

0,659127075

-18180,134

-1,203194706

-420,4183545

-0,02782406

-56425,86082

-3,73436725

4968,663854

0,328835312

-7420,610567

-0,491109656

-16701,8071

-1,105356313

-14776,60843

-0,977943124

12016,85173

0,79529735

14074,4467

0,931472769

-17259,96334

-1,142296119

4573,595548

0,302688965

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

47

48

49

50

51

52

53

54

55

56

57

58

59

60

61

62

63

64

204575,7275

141761,3827

154428,3801

225035,9276

146359,1966

295887,0256

164307,8512

189004,1206

211041,076

156969,2823

182556,1319

155096,0837

161186,1462

151730,1574

162497,6838

218345,2731

245561,8194

212601,4668

212368,2976

249114,1183

161910,7633

124228,8634

165393,6841

207013,2599

155532,873

158114,9974

224068,2313

157318,164

210136,6508

185741,0533

173640,7855

223960,5125

156285,8055

156977,5107

312168,7144

295192,3057

152183,0835

181870,4922

158950,9284

192225,1236

224718,328

152327,5066

219961,9222

169255,1938

217973,6639

198582,3391

175486,8484

-18575,72752

11738,61733

11571,61986

-135,9275779

12140,80339

36112,97441

7692,14883

-13004,12057

-1041,...

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