Question

Selling Price        Living Area (Sq Feet)       No. Bathrooms No Bedrooms    Age (Years)

$240,000              2,022     2.5          3              20

$235,000              1,578     2              3              20

$500,075              3,400     3              3              20

$240,000              1,744     2.5          3              20

$270,000              2,560     2.5          3              20

$225,000              1,398     2.5          3              20

$280,000              2,494     2.5          3              20

$225,000              2,208     2.5          4              20

$248,220              2,550     2.5          3              20

$275,000              1,812     2.5          2              20

$137,000              1,290     1              2              20

$150,000              1,172     2              2              20

$649,000              4,128     3.5          3              20

$195,000              1,816     2.5          3              97

$373,200              2,628     2.5          4              20

$169,450              1,254     2.5          3              20

$144,200              1,660     1.5          4              20

$189,900              1,850     1.5          3              20

$166,000              1,258     2              3              20

$160,000              1,219     2              3              20

$327,355              1,850     2.5          3              20

$247,000              2,103     2.5          3              20

$318,000              1,806     2.5          3              20

$341,000              1,674     1.5          2              17

$288,650              2,242     2.5          3              20

$157,000              1,408     1.5          3              20

$449,000              3,457     2.5          3              21

$142,000              1,728     1.5          3              21

$389,000              2,354     2.5          3              21

$476,000              2,246     2.5          3              21

$249,230              1,902     2.5          2              21

$139,900              1,178     1              3              21

$301,900              2,896     3.5          4              21

$425,000              2,457     3              3              41

$121,000              936         1              3              50

$150,000              934         1              2              21

$138,000              1,279     1              3              21

$199,900              1,888     2              3              26

$145,000              1,686     1.5          4              21

$465,000              2,310     3              2              21

$158,000              1,200     1.5          3              21

1.             Develop a multiple linear regression model to predict the price of a house using the square feet of living area, number of bedrooms, number of bathrooms, and age as the predictor variables.

1.             Write the reqression equation.
2.             Discuss the statistical significance of the model as a whole using the appropriate regression statistic at a 95% level of confidence.
3.              Discuss the statistical significance of the coefficient for each independent variable using the appropriate regression statistics at a 95% level of confidence.
4.             Discuss the statistical significance of the coefficient for each independent variable using the appropriate regression statistics at a 90% level of confidence.

2.             Develop a multiple linear regression model to predict the price of a house using the square feet of living area, number of bedrooms, and number of bathrooms as the predictor variables.

1.             Write the reqression equation.
2.             Discuss the statistical significance of the model as a whole using the appropriate regression statistic at a 95% level of confidence.
3.              Discuss the statistical significance of the coefficient for each independent variable using the appropriate regression statistics at a 95% level of confidence.
4.             Interpret the coefficient for each independent variable.
5.             What percentage of the observed variation in housing prices is explained by the model?
6.              Determine the prediction interval of a house with 3,000 square feet of living area, 3 bedrooms, and 2.5 bathrooms, and comment on the prediction interval.

3.             In Case Study No.1 you ran a simple linear regression model for predicting the price of a house based upon its living area in square feet using a 95% level of confidence. Rerun that simple linear regression model for predicting the price of a house based upon its living area in square feet using the Case study 2 data using a 95% level of confidence. Compare the regression statistics for this simple linear regression model with the statistics for the preceding multiple linear regression model using square feet of living area, number of bedrooms, and number of bathrooms as the predictor variables. Which model is the preferred model at a 95% level of confidence? Use the Significance F values, p-values for the independent variables, R-squared or Adjusted R-squared values (as appropriate), and standard errors to explain your selection.

Prepare a single Microsoft Excel file to document your regression analyses. Prepare a single Microsoft Word document that outlines your responses for each portion of the case study.

Answer 1

data

selling price	sq-feet	no. of bathroom	no. of bedroom	age
240000	2022	2.5	3	20
235000	1578	2	3	20
500075	3400	3	3	20
240000	1744	2.5	3	20
270000	2560	2.5	3	20
225000	1398	2.5	3	20
280000	2494	2.5	3	20
225000	2208	2.5	4	20
248220	2550	2.5	3	20
275000	1812	2.5	2	20
137000	1290	1	2	20
150000	1172	2	2	20
649000	4128	3.5	3	20
195000	1816	2.5	3	97
373200	2628	2.5	4	20
169450	1254	2.5	3	20
144200	1660	1.5	4	20
189900	1850	1.5	3	20
166000	1258	2	3	20
160000	1219	2	3	20
327355	1850	2.5	3	20
247000	2103	2.5	3	20
318000	1806	2.5	3	20
341000	1674	1.5	2	17
288650	2242	2.5	3	20
157000	1408	1.5	3	20
449000	3457	2.5	3	21
142000	1728	1.5	3	21
389000	2354	2.5	3	21
476000	2246	2.5	3	21
249230	1902	2.5	2	21
139900	1178	1	3	21
301900	2896	3.5	4	21
425000	2457	3	3	41
121000	936	1	3	50
150000	934	1	2	21
138000	1279	1	3	21
199900	1888	2	3	26
145000	1686	1.5	4	21
465000	2310	3	2	21
158000	1200	1.5	3	21

a)

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.890990637
R Square	0.793864316
Adjusted R Square	0.770960351
Standard Error	58681.22233
Observations	41
ANOVA
	df	SS	MS	F	Significance F
Regression	4	4.77413E+11	1.19353E+11	34.66056288	6.90482E-12
Residual	36	1.23965E+11	3443485854
Total	40	6.01378E+11
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	91934.57151	57728.62547	1.592530062	0.120009481	-25144.50748	209013.6505
sq-feet	129.2855885	20.82894503	6.207015682	3.67893E-07	87.04252999	171.5286469
no. of bathroom	39969.87177	21376.02784	1.869845608	0.069655054	-3382.722058	83322.4656
no. of bedroom	-54284.86462	17629.8245	-3.079149461	0.003959575	-90039.80593	-18529.92331
age	-359.3853607	718.6420902	-0.500089496	0.620055382	-1816.859073	1098.088351

y^ = 91934.5715 + 129.2856 * sq-feet + 39969.8718 * no.of bathroom -54284.8646*no, of bedroom -359.3854*age

b)

p-value = 6.90482E-12 < 0.05

hence the model is significant

c)

if p-value < alpha

the variable is significant

here sq-feet and no. of bedroom have p-value < 0.05

hence they are significant at 95 % level

d)

apart from sq-feet and no. of bedroom ,no. of bathroom have p-value < 0.10

hence these three are significant at 90% confidence level

e) R^2 = 0.793864316

hence 79.39%