# Solution Doc

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User Generated
Subject
Statistics
School
Alabama Southern Community College
Type
Homework
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1
We will work with the data for homes for sale in Lafayette and West Lafayette, Indiana. The response
(dependent) variable is Price, the asking price of a home. The data set contains the following explanatory
(independent) variables:
SqFt, the number of square feet for the home
Bedrooms, the number of bedrooms
Baths, the number of bathrooms
Garage, the number of cars that can fit in the garage
1. The data set contains 45 homes for sale in zip code 47904. a few homes have prices that are
somewhat high relative to the others. Similarly, some values for SqFt are relatively high. Exclude
any home with Price greater than \$150,000 and any home with SqFt greater than 1800 ft
2
. After
excluding process, how many houses do you have in the data set? (3p)
Number of houses = 35
Show the observations that excluded (2p)
Id
Price (\$ thousands)
SqFt
Baths
Bedrooms
Garage
23
74,973
2186
1.5
4
2
33
160,450
2050
2
3
2
36
225,347
1605
2.5
3
2
37
125,753
2035
3
3
2
39
200,500
1928
3
3
2
40
128,506
2091
1.5
3
2
41
174,367
2100
2
2
2
42
179,809
2246
2.5
5
2
43
205,450
1851
2
2
2
45
128,894
2296
2.5
3
3
2. Regress price (dependent variable) on square feet (independent variable):
Excel Output (5p)
SUMMARY
OUTPUT
Regression Statistics

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2
Multiple R
R Square
Standard Error
Observations
ANOVA
SS
MS
F
Significance
F
Regression
2.66E+09
2.66E+09
14.45457
0.000588
Residual
6.08E+09
1.84E+08
Total
8.74E+09
Standard
Error
t Stat
P-value
Lower 95%
Upper
95%
Intercept
9571.337
5.070465
1.5E-05
29058.1
68004.17
SqFt
8.0991
3.801916
0.000588
14.31436
47.26984
a. Write the regression equation. (2p)
Price (\$ thousands) = 48531.1346 + 30.7921*SqFt
b. What proportion of the variance in Price variable can be explained by the Square Feet
variable? Is this proportion of variance statistically significant at .05 level of
Proportion of variance explained = R Squared = 0.3046
As a percent
= 0.3046*100%
= 30.46%
Is this proportion of variance statistically significant at .05 level of significance?
Yes
Since p-value, 0.0006 is less than the significance level, 0.05, there is a significant
linear relationship between Price and Square Feet. This means that the proportion
of variance explained is significant.
c. Does Square feet significantly predict the price of the house? Justify your answer. (3p)
Since
Yes. This is because the p-value of Square feet, 0.0006 is less than the significance
level of 0.05 hence being significant predictor.
3. Recode the “Bedrooms” categorical variable to be Bed3 = 1 if the home has three or more
bedrooms and Bed3 = 0 if it does not. Bed3 is called as Dummy variable (indicator variable).
Excel Output (5p)

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We will work with the data for homes for sale in Lafayette and West Lafayette, Indiana. The response (dependent) variable is Price, the asking price of a home. The data set contains the following explanatory (independent) variables: • SqFt, the number of square feet for the home • Bedrooms, the number of bedrooms • Baths, the number of bathrooms • Garage, the number of cars that can fit in the garage 1. The data set contains 45 homes for sale in zip code 47904. a few homes have prices that are somewhat high relative to the others. Similarly, some values for SqFt are relatively high. Exclude any home with Price greater than \$150,000 and any home with SqFt greater than 1800 ft2. After excluding process, how many houses do you have in the data set? (3p) Number of houses = 35 Show the observations that excluded (2p) Id Price (\$ thousands) SqFt Baths Bedrooms Garage 23 74,973 2186 1.5 4 2 33 160,450 2050 2 3 2 36 225,347 1605 2.5 3 2 37 125,753 2035 3 3 2 39 200,500 1928 3 3 2 40 128,506 2091 1.5 3 2 41 174,367 2100 2 2 2 42 179,809 2246 2.5 5 2 43 205,450 1851 2 2 2 45 128,894 2296 2.5 3 3 2. Regress price (dependent variable) on square feet (independent variable): Excel Output (5p) SUMMARY OUTPUT Regression Statistics 1 Multiple R R Square Adjusted R Square Standard Error Observations 0.551903984 0.304598007 0.283525219 13569.60577 35 ANOVA df Regression Residual Total Intercept SqFt 1 33 34 Coefficients 4853 ...
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