Final Project Assignment

However the variation in selling price of the homes with garage is much larger (almost double) than the homes without garage.

2.) Refer to the real estate data and develop the following confidence intervals:

1. Develop a 95 percent confidence interval for the mean selling price of the homes.

The obtained Minitab output is given below,

One-Sample T: Price, Distance

Variable N Mean StDev SE Mean 95% CI

Price 105 221.10 47.11 4.60 (211.99, 230.22)

From the above output we can see that the 95 percent confidence interval for the mean selling price of the homes is (211.99, 230.22).

1. Develop a 95 percent confidence interval for the mean distance the home is from the center of the city.

The obtained Minitab output is given below,

One-Sample T: Price, Distance

Variable N Mean StDev SE Mean 95% CI

Distance 105 14.629 4.874 0.476 (13.685, 15.572)

From the above output we can see that the 95 percent confidence interval for the mean distance the home is from the center of the city is (13.685, 15.572)

3.) Refer to the Real Estate data in Blackboard. 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.

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

The obtained regression output is given below,

Regression Analysis: Price versus Bedrooms, Size, Pool, Distance, Twnship, Garage, Baths

Analysis of Variance

Source DF Adj SS Adj MS F-Value P-Value

Regression 7 123136 17590.9 15.85 0.000

Bedrooms 1 8998 8997.9 8.11 0.005

Size 1 7605 7604.9 6.85 0.010

Pool 1 7980 7979.8 7.19 0.009

Distance 1 2070 2070.2 1.87 0.175

Twnship 1 460 460.5 0.42 0.521

Garage 1 23731 23731.4 21.39 0.000

Baths 1 7211 7211.3 6.50 0.012

Error 97 107631 1109.6

Total 104 230768

Model Summary

S R-sq R-sq(adj) R-sq(pred)

33.3106 53.36% 49.99% 45.11%

Coefficients

Term Coef SE Coef T-Value P-Value VIF

Constant 43.1 39.7 1.09 0.280

Bedrooms 7.38 2.59 2.85 0.005 1.42

Size 0.0386 0.0148 2.62 0.010 1.26

Pool 19.11 7.13 2.68 0.009 1.11

Distance -1.013 0.741 -1.37 0.175 1.22

Twnship -1.74 2.70 -0.64 0.521 1.13

Garage 35.50 7.68 4.62 0.000 1.22

Baths 23.09 9.06 2.55 0.012 1.19

Regression Equation

Price = 43.1 + 7.38 Bedrooms + 0.0386 Size + 19.11 Pool - 1.013 Distance - 1.74 Twnship

+ 35.50 Garage + 23.09 Baths

Fits and Diagnostics for Unusual Observations

Obs Price Fit Resid Std Resid

46 307.80 238.00 69.80 2.29 R

57 176.00 241.48 -65.48 -2.02 R

105 188.30 272.91 -84.61 -2.65 R

R Large residual

From the above output we can see that the regression equation is,

Price = 43.1 + 7.38 Bedrooms + 0.0386 Size + 19.11 Pool - 1.013 Distance - 1.74 Twnship + 35.50 Garage + 23.09 Baths

Thus a garage adds 35.50 and an extra bathroom adds 23.09 on an average to the selling price of a home.

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

The R-squared value is 53.36% or 0.5336 which implies that 53.36% of the variation in selling price is getting explained by the above regression model.

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

The obtained correlation matrix is given below,

Correlation: Price, Bedrooms, Size, Pool, Distance, Twnship, Garage, Baths

Price Bedrooms Size Pool Distance Twnship Garage

Bedrooms 0.467

0.000

Size 0.371 0.383

0.000 0.000

Pool 0.294 0.005 0.201

0.002 0.957 0.040

Distance -0.347 -0.153 -0.117 -0.139

0.000 0.118 0.234 0.156

Twnship 0.128 0.200 0.185 0.201 -0.209

0.193 0.041 0.059 0.040 0.033

Garage 0.526 0.234 0.083 0.114 -0.359 0.057

0.000 0.016 0.400 0.246 0.000 0.566

Baths 0.382 0.329 0.024 0.055 -0.195 0.050 0.221

0.000 0.001 0.805 0.581 0.046 0.615 0.023

Cell Contents: Pearson correlation

P-Value

The above output indicates that except Twnship, all other variables have significant correlation with the dependent variable selling price. However none of the correlation is strong.