Download Solution: a. Data analysis using descriptive statistics 1) Calculate the

Solution:
a. Data analysis using descriptive statistics
1) Calculate the measures of central tendency, dispersion, and skew for your data
The descriptive statistics for Price is given below
Using Microsoft Excel 2007
Add- Ins
Megastat
Descriptive Statistics
count
mean
sample variance
sample standard deviation
minimum
maximum
range
sum
sum of squares
deviation sum of squares
(SSX)
population variance
population standard
deviation
standard error of the mean
skewness
kurtosis
coefficient of variation
Price
105
221.103
2,218.919
47.105
125
345.3
220.3
23,215.800
5,363,847.300
230,767.589
2,197.787
46.881
4.597
0.474
-0.277
21.30%
(CV)
1st quartile
median
3rd quartile
interquartile range
mode
187.000
213.600
251.400
64.400
188.300
The descriptive statistics for Size
Using Microsoft Excel 2007
Add- Ins
Megastat
Descriptive Statistics
count
mean
sample variance
sample standard deviation
minimum
maximum
range
sum
sum of squares
deviation sum of squares
(SSX)
population variance
population standard
deviation
standard error of the mean
skewness
kurtosis
coefficient of variation
(CV)
Size
105
2,223.81
61,831.50
248.66
1600
2900
1300
233,500.00
525,690,000.00
6,430,476.19
61,242.63
247.47
24.27
0.32
0.60
11.18%
1st quartile
median
3rd quartile
interquartile range
mode
2,100.00
2,200.00
2,400.00
300.00
2,100.00
The descriptive statistics for Bedrooms
Using Microsoft Excel 2007
Add- Ins
Megastat
Descriptive Statistics
count
minimum
maximum
range
Bedrooms
105
2
8
6
1st quartile
median
3rd quartile
interquartile range
mode
The descriptive statistics for Distance
Using Microsoft Excel 2007
Add- Ins
Megastat
Descriptive Statistics
3.00
4.00
5.00
2.00
4.00
count
mean
sample variance
sample standard deviation
minimum
maximum
range
sum
sum of squares
deviation sum of squares
(SSX)
Distance
105
14.63
23.75
4.87
6
28
22
1,536.00
24,940.00
2,470.51
population variance
population standard
deviation
23.53
4.85
standard error of the mean
0.48
skewness
kurtosis
coefficient of variation
(CV)
0.40
-0.17
33.32%
1st quartile
median
3rd quartile
interquartile range
mode
11.00
15.00
18.00
7.00
16.00
The descriptive statistics for Twnship
Using Microsoft Excel 2007
Add- Ins
Megastat
Descriptive Statistics
Twnship
count
minimum
maximum
range
1st quartile
median
3rd quartile
interquartile range
mode
105
1
5
4
count
minimum
maximum
range
2.00
3.00
4.00
2.00
4.00
Baths
105
1.5
3
1.5
1st quartile
median
3rd quartile
interquartile range
mode
2.000
2.000
2.000
0.000
2.000
2) Display your descriptive statistical data using graphic and tabular techniques
a) Line graph
The line diagram for the bedrooms in the given data
b) Bar graph
The bar diagram for the price of the house is shown below
The bar diagram for the size of the house is shown below
3) based on your measures of central tendency and graphs, discuss the best measures of
central tendency and dispersion of your data. Justify your selection
From the measures of central tendency there is no need for justification because the
calculation which are important for the variables are analyzed in the descriptive statistics part.
b. Conclusions
Discuss whether your research findings answered your problem statement (research
question), or whether more research might be necessary
The regression analysis will be valid and apt test for our research
Where
The dependent variable
Y = Price
The independent variables
X1: Bedrooms
X2: Size
X3: Pool
X4: Distance
X5: Twnship
X6: Garage
X7: Baths
So the corresponding regression coefficients as 1 , 2, 3 , 4, 5 , 6 and 7
Hypothesis:
Null hypothesis:
H0: The regression coefficients of Bedrooms, Size, Pool, Distance, Twnship, Garage and Baths
are equal to zero
Alternative hypothesis:
H1: At least one of the regression coefficients of Bedrooms, Size, Pool, Distance, Twnship,
Garage and Baths are not equal to zero
So using Microsoft excel we can find the multiple regression equation the steps involved to solve
is shown below
Data
Data Analysis
Regression
The solution of Microsoft excel is shown below
SUMMARY OUTPUT
Regression Statistics
Multiple R
0.730476
R Square
0.533595
Adjusted R
Square
0.499937
Standard
Error
33.31064
Observations
105
ANOVA
df
Regression
Residual
Total
Intercept
Bedrooms
Size
Pool
Distance
Twnship
Garage
Baths
SS
MS
17590.9
3
1109.59
9
F
15.8534
1
Significanc
eF
7
123136.5
97
104
107631.1
230767.6
Coefficient
s
62.24869
7.375498
0.038627
Standard
Error
40.91404
2.590021
0.014755
t Stat
1.52145
2.84765
2.61795
P-value
0.1314
0.00537
0.01026
Lower 95%
-18.9544
2.235023
0.009343
Upper
95%
143.451
12.5159
0.06791
Lower
95.0%
-18.9544
2.235023
0.009343
Upper
95.0%
143.451
12.5159
0.06791
-19.1114
-1.01267
-1.73901
35.49802
23.09255
7.126553
0.741385
2.699416
7.675838
9.058308
-2.6817
-1.3659
-0.6442
4.62464
2.54932
0.00861
0.17512
0.52095
1.16E-0
0.01236
-33.2557
-2.48411
-7.0966
20.2636
5.114313
-4.9672
0.45877
3.61858
50.7324
41.0707
-33.2557
-2.48411
-7.0966
20.2636
5.114313
-4.9672
0.45877
3.61858
50.7324
41.0707
The linear regression equation is
1.01E-13
Y =62.24869 +7.375498 X1+0.038627 X2-19.1114 X3-1.01267 X4-1.73901 X5+35.49802 X6+23.09255 X7
Conclusion:
Since the p-value is less than the test statistic value there is no evidence to accept the null
hypothesis. Hence we conclude that at least one of the regression coefficients of Bedrooms, Size,
Pool, Distance, Twnship, Garage and Baths are not equal to zero