Refer to the Real Estate data. Use the selling price of the home as the dependen

ID: 3157906 • Letter: R

Question

Refer to the Real Estate data. Use the selling price of the home as the dependent variable and determine the regression equation with the numbers of bedrooms, size of the house, whether there is a pool, distance from the center of the city, township, whether there is an attached garage, and the number of bathrooms as independent variables.

Write out the regression equation. How much does a garage or an extra bathroom add to the selling price of a home?

Determine the value of R-squared. Provide an interpretation of the variance R-squared represents.

Develop a correlation matrix. Which independent variables have strong or weak correlations with the dependent variable (price)?

Price Bedrooms Square Feet Pool Distance Township Garage Baths 245,400 2 2100 0 12 1 1 2 221,100 3 2300 0 18 1 0 1.5 232,200 3 1900 0 16 1 1 1.5 198,300 4 2100 0 19 1 1 1.5 192,600 6 2200 0 14 1 0 2 147,400 6 1700 0 12 1 0 2 224,000 3 1900 0 6 1 1 2 220,900 2 2300 0 12 1 1 2 199,000 3 2500 0 18 1 0 1.5 139,900 2 2100 1 28 1 0 1.5 224,800 3 2200 1 17 1 1 2.5 216,800 3 2200 1 15 1 1 2 176,000 4 2200 1 15 1 1 2 189,400 4 2200 1 24 1 1 2 125,900 2 2400 1 28 1 0 1.5 192,900 4 1900 0 14 2 1 2.5 166,200 3 2000 0 16 2 1 2 307,800 3 2400 0 21 2 1 3 209,700 5 2200 0 13 2 1 2 207,500 3 2100 0 10 2 0 2 209,700 4 2200 0 19 2 1 2 173,600 4 2100 0 14 2 1 2.5 188,300 6 2100 0 14 2 1 2.5 213,600 2 2200 1 16 2 0 2.5 271,800 2 2100 1 9 2 1 2.5 281,300 3 2100 1 16 2 1 2 247,700 5 2400 1 16 2 1 2 216,000 4 2300 1 19 2 0 2 273,200 5 2200 1 16 2 1 3 251,400 3 1900 1 12 2 1 2 154,300 2 2000 1 13 2 0 2 294,000 2 2100 1 13 2 1 2.5 192,200 2 2400 1 16 2 0 2.5 244,600 2 2300 1 9 2 1 2.5 253,200 3 2300 1 16 2 1 2 172,700 4 2200 0 16 3 0 2 206,000 3 2100 0 9 3 0 1.5 166,500 3 1600 0 19 3 0 2.5 190,900 3 2200 0 18 3 1 2 254,300 4 2500 0 15 3 1 2 176,300 2 2000 0 17 3 0 2 155,400 4 2400 0 16 3 0 2 242,100 3 2300 1 12 3 0 2 327,200 6 2500 1 15 3 1 2 292,400 4 2100 1 14 3 1 2 246,100 4 2100 1 18 3 1 2 194,400 2 2300 1 11 3 0 2 233,000 3 2200 1 14 3 1 1.5 234,000 2 1700 1 19 3 1 2 199,800 3 2100 1 19 3 1 2 236,400 5 2200 1 20 3 1 2 172,400 3 2200 1 23 3 0 2 246,000 6 2300 1 7 3 1 3 312,100 7 2400 1 13 3 1 3 289,800 6 2000 1 21 3 1 3 217,800 3 2500 1 12 3 0 2 294,500 6 2700 1 15 3 1 2 263,200 4 2300 1 14 3 1 2 221,500 4 2300 1 18 3 1 2 175,000 2 2500 1 11 3 0 2 207,500 5 2300 0 21 4 0 2.5 198,900 3 2200 0 10 4 1 2 209,300 6 1900 0 15 4 1 2 182,700 4 2000 0 14 4 0 2.5 205,100 3 2000 0 20 4 0 2 175,600 4 2300 0 24 4 1 2 171,600 3 2000 0 16 4 0 2 269,900 5 2200 0 11 4 1 2.5 186,700 5 2500 0 21 4 0 2.5 179,000 3 2400 0 10 4 1 2 188,300 6 2100 0 15 4 1 2 182,400 4 2100 1 19 4 0 2 266,600 4 2400 1 13 4 1 2 209,000 2 1700 1 8 4 1 1.5 270,800 6 2500 1 7 4 1 2 252,300 4 2600 1 8 4 1 2 345,300 8 2600 1 9 4 1 2 187,000 2 1900 1 26 4 0 2 257,200 2 2100 1 9 4 1 2 294,300 7 2400 1 8 4 1 2 125,000 2 1900 1 18 4 0 1.5 164,100 4 2300 1 19 4 0 2 240,000 4 2600 1 13 4 1 2 188,100 2 1900 1 8 4 1 1.5 243,700 6 2700 1 7 4 1 2 227,100 4 2900 1 8 4 1 2 310,800 8 2900 1 9 4 1 2 179,000 3 2400 1 8 4 1 2 173,600 4 2100 1 9 4 1 2 263,100 4 2300 0 17 5 1 2 173,100 2 2200 0 21 5 1 1.5 236,800 4 2600 0 17 5 1 2 209,300 5 2100 1 20 5 0 1.5 326,300 6 2100 1 11 5 1 3 180,400 2 2000 1 11 5 0 2 207,100 2 2000 1 11 5 1 2 177,100 2 1900 1 10 5 1 2 312,100 6 2600 1 7 5 1 2.5 269,200 5 2200 1 8 5 1 3 228,400 3 2300 1 17 5 1 1.5 222,100 2 2100 1 9 5 1 2 188,300 5 2300 1 20 5 0 1.5 293,700 6 2400 1 11 5 1 3 227,100 4 2900 1 20 5 0 1.5 188,300 5 2300 1 11 5 1 3

Explanation / Answer

Write out the regression equation. How much does a garage or an extra bathroom add to the selling price of a home?

Regression Analysis

R²

0.534

Adjusted R²

0.500

105

0.730

Std. Error

33310.645

Dep. Var.

Price

ANOVA table

Source

p-value

Regression

123,136,480,136.3900

17,590,925,733.7700

15.85

1.01E-13

Residual

107,631,109,006.4670

1,109,599,061.9223

Total

230,767,589,142.8570

104

Regression output

confidence interval

variables

coefficients

std. error

t (df=97)

p-value

95% lower

95% upper

Intercept

43,137.2499

39,739.2782

1.086

.2804

-35,734.2170

122,008.7167

Bedrooms

7,375.4976

2,590.0212

2.848

.0054

2,235.0226

12,515.9727

Square Feet

38.6270

14.7546

2.618

.0103

9.3431

67.9108

Pool

19,111.4418

7,126.5527

2.682

.0086

4,967.2074

33,255.6762

Distance

-1,012.6688

741.3847

-1.366

.1751

-2,484.1123

458.7746

Township

-1,739.0078

2,699.4164

-0.644

.5210

-7,096.6020

3,618.5864

Garage

35,498.0189

7,675.8385

4.625

1.16E-05

20,263.6043

50,732.4335

Baths

23,092.5459

9,058.3077

2.549

.0124

5,114.3125

41,070.7792

Price = 43,137.2499 +7,375.4976 *Bedrooms+ 38.6270 *Square Feet+ 19,111.4418 *Pool -1,012.6688 *Distance -1,739.0078 *Township+ 35,498.0189 *Garage+ 23,092.5459 *Baths

Presence of garage in the home increases the price by $35,498.0189.

If one bath room increases in the home will increase the price by $23,092.5459.

Determine the value of R-squared. Provide an interpretation of the variance R-squared represents.

R-squared =0.534

53.4% of variance in price is explained by the model.

Develop a correlation matrix. Which independent variables have strong or weak correlations with the dependent variable (price)?

Correlation Matrix

Price

Bedrooms

Square Feet

Pool

Distance

Township

Garage

Baths

Price

1.000

Bedrooms

.467

1.000

Square Feet

.371

.383

1.000

Pool

.294

.005

.201

1.000

Distance

-.347

-.153

-.117

-.139

1.000

Township

.128

.200

.185

.201

-.209

1.000

Garage

.526

.234

.083

.114

-.359

.057

1.000

Baths

.382

.329

.024

.055

-.195

.050

.221

1.000

105

sample size

± .192

critical value .05 (two-tail)

Correlation between Price and Garage is strong, r=0.526.

Correlation between Price and Township is weak, r=0.128.

Regression Analysis

R²

0.534

Adjusted R²

0.500

105

0.730

Std. Error

33310.645

Dep. Var.

Price

ANOVA table

Source

p-value

Regression

123,136,480,136.3900

17,590,925,733.7700

15.85

1.01E-13

Residual

107,631,109,006.4670

1,109,599,061.9223

Total

230,767,589,142.8570

104

Regression output

confidence interval

variables

coefficients

std. error

t (df=97)

p-value

95% lower

95% upper

Intercept

43,137.2499

39,739.2782

1.086

.2804

-35,734.2170

122,008.7167

Bedrooms

7,375.4976

2,590.0212

2.848

.0054

2,235.0226

12,515.9727

Square Feet

38.6270

14.7546

2.618

.0103

9.3431

67.9108

Pool

19,111.4418

7,126.5527

2.682

.0086

4,967.2074

33,255.6762

Distance

-1,012.6688

741.3847

-1.366

.1751

-2,484.1123

458.7746

Township

-1,739.0078

2,699.4164

-0.644

.5210

-7,096.6020

3,618.5864

Garage

35,498.0189

7,675.8385

4.625

1.16E-05

20,263.6043

50,732.4335

Baths

23,092.5459

9,058.3077

2.549

.0124

5,114.3125

41,070.7792

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Refer to the Real Estate data. Use the selling price of the home as the dependen

Refer to the Real Estate data. Use the selling price of the home as the dependen

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