A real estate agent wanted to find the relationship between sale price of houses and the size of the house. Shecollected data on two variables recorded in the following table for 15 houses in Seattle. The two variables are PRICE= Sale price of houses in thousands of dollars SIZE= Area of the entire house in square feet. The Excel working has been given. Note: the left hand side is Regression run.. The right hand side is 'new' regression run (for ans d). Question a) Using MICROSOFT EXCEL- run the above regression and copy the output into your assignment word document from which you can write down the least square regression line. Write down the least square regression line from that specific output. b) Interpret the slope and constant term with proper UNITS assigned. c) Comment on the explanatory power of the regression model from the required output. Copy that specific output into your assignment word document.
Correlation
Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.
Linear Correlation
A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related.
Regression Analysis
Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.
A real estate agent wanted to find the relationship between sale price of houses and the size of the house. Shecollected data on two variables recorded in the following table for 15 houses in Seattle. The two variables are
PRICE= Sale price of houses in thousands of dollars
SIZE= Area of the entire house in square feet.
The Excel working has been given.
Note: the left hand side is Regression run.. The right hand side is 'new' regression run (for ans d).
Question
a) Using MICROSOFT EXCEL- run the above regression and copy the output into your assignment word document
from which you can write down the least square regression line. Write down the least square regression line
from that specific output.
b) Interpret the slope and constant term with proper UNITS assigned.
c) Comment on the explanatory power of the regression model from the required output. Copy that specific
output into your assignment word document.
Now to increase the explanatory power of the model the real estate agent decides to look at the age of the
house and the garden size. For the 15 houses in our sample the new variables are
AGE= Age of the house in years, since it was built
GARDEN= Area of the garden in acres.
d) Once these two new variables are added- run the new regression using MICROSOFT EXCEL. Copy the output
into your assignment word document from which you can write down the new least square regression line.
Write down the new least square regression line from that specific output.
e) Interpret the coefficients with all the independent variables with proper UNITS.
f) Comment on the explanatory power of the regression model from the required output. Copy the output into
your assignment word document.
g) Compare the two regression models that you have found using the appropriate parameter. Which is better
and why?
h) If you were to add a DUMMY VARIABLE in this regression model what would be an appropriate one? Why?
Give sound logical reasoning
![Price
Size
Age(in years)
Garzen(acres)
Price
Size
455
2500
8
1.4
455
2500
278
2250
12
0.9
278
2250
463
2900
5
1.8
463
2900
327
1800
9
0.7
327
1800
505
3200
4
2.6
505
3200
264
2400
28
1.2
264
2400
445
2700
2.1
445
2700
346
2050
13
1.1
346
2050
487
2850
7
2.8
487
2850
289
2400
16
1.6
289
2400
434
2600
5
3.2
434
2600
411
2300
8
1.7
411
2300
223
1700
19
0.5
223
1700
323
2300
17
2.7
323
2300
488
2980
9
3.4
488
2980
SUMMARY OUTPUT
SUMMARY OUTPUT
Regression Statistics
Multiple R
R Square
Adjusted R Square
Standard Error
Regression Statistics
0.944818162
Multiple R
R Square
Adjusted R Square
Standard Error
0.82296733
0.89268136
0.677275227
0.86341264
0.652450244
34.67810626
55.31699902
Observations
15
Observations
15
ANOVA
Significance F
1.25486E-05
ANOVA
df
SS
MS
df
SS
MS
Significance F
Regression
110033.4517
36677.8 30.4995
Regression
83482.11839
83482.11839 27.2820021
0.000164323
Residual
11
13228.28159
1202.57
Residual
13
39779.61495
3059.97038
Total
14
123261.7333
Total
14
123261.7333
Coefficients
Standard Error
t Stat
P-value
Lower 95%
Upper 95% Lower 95.0% Upper 95.0%
15.41179707 367.20378 15.4117971 367.2037815
Coefficients
Standard Error
t Stat
P-value
Lower 95%
Upper 95%
Lower 95.0% Upper 95.0%
Intercept
191.3077893
79.91693694 2.39383 0.03562
86.86812572
Intercept
Size
-65.0227611
-0.748522667 0.46747219
-252.6899371 122.6444149 -252.6899371 122.6444149
Size
0.103040893
0.035378469 2.91253 0.01412
0.025173407 0.1809084 0.02517341 0.180908379
Age(in years)
Garzen(acres)
0.181785579
0.034803371
5.223217602 0.00016432
0.106597467
0.25697369 0.106597467
0.25697369
-7.57059389
1.67100526 -4.53056 0.00086
-11.24845167 -3.8927361 -11.2484517 -3.89273611
12.36510295
15.74732647 0.78522 0.44891
-22.29452891
47.024735 -22.2945289 47.02473482](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F96bf0899-413e-4743-a96f-62e645affcf4%2F9992e6c5-ff8c-4673-a5e8-80979d09b599%2Fbvafdt_processed.png&w=3840&q=75)
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