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(ans a).. The right hand side is 'new' regression run (for ans d). Question 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. (The excel work has been given above, please answer the rest, if any) e) Interpret the coefficients with all the independent variables with proper UNITS

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.6: Summarizing Categorical Data
Problem 35PPS
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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(ans a).. The right hand side is 'new' regression run (for ans d).

Question

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. (The excel work has been given above, please answer the rest, if any)

e) Interpret the coefficients with all the independent variables with proper UNITS.

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
Transcribed Image Text: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
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