Homework SourseThe Rent in the sample range from 15500 to 32000 and the off
The Rent in the sample range from $15,500 to $32,000 and the office sizes in the sample range from 740 to 1,260 square feet. The output from th e Excel regression is provided below. PLease provide detail explaination...thanks
1. At the 0.05 level of significance, is there evidence of a linear relationship between the rent and square footage? Explain.
2. You are considering signing a lease for an office of 1000 sq ft in the same neighborhood.The rent is $21,975. Is this reasonable based on the prediction from the regression model? Why or why not?
3. You are considering signing a lease for a small office in the same neighborhood. The space is 400 sq ft. Can you use this model to predict the monthly rent for that apartment?Why or why not?
SUMMARY OUTPUT
Regression Statistics
Multiple R
0.82049999
R Square
0.67322024
Adjusted R Square
0.66195197
Standard Error
3042.5153
Observations
31
ANOVA
df
SS
MS
F
Significance F
Regression
1
553051465.6
5.53E+08
59.7447854
1.59606E-08
Residual
29
268450081.2
9256899
Total
30
821501546.8
Coefficients
Standard Error
t Stat
P-value
Lower 95%
Upper 95%
Intercept
-2010.5068
3349.105517
-0.7777
0.44304505
-9454.286633
4245.093122
Size(Sq Ft)
25.0017135
3.193582115
7.729475
1.5961E-08
18.15310465
31.21632226
| SUMMARY OUTPUT | ||||||
| Regression Statistics | ||||||
| Multiple R | 0.82049999 | |||||
| R Square | 0.67322024 | |||||
| Adjusted R Square | 0.66195197 | |||||
| Standard Error | 3042.5153 | |||||
| Observations | 31 | |||||
| ANOVA | ||||||
| df | SS | MS | F | Significance F | ||
| Regression | 1 | 553051465.6 | 5.53E+08 | 59.7447854 | 1.59606E-08 | |
| Residual | 29 | 268450081.2 | 9256899 | |||
| Total | 30 | 821501546.8 | ||||
| Coefficients | Standard Error | t Stat | P-value | Lower 95% | Upper 95% | |
| Intercept | -2010.5068 | 3349.105517 | -0.7777 | 0.44304505 | -9454.286633 | 4245.093122 |
| Size(Sq Ft) | 25.0017135 | 3.193582115 | 7.729475 | 1.5961E-08 | 18.15310465 | 31.21632226 |
Solution
The The Rent in the sample range from $15,500 to $32,000 and the office sizes in the sample range from 740 to 1,260 Square feet. The output from the Excel regression is provided below. Answer the follow questions (1) and (2).
Coefficients
Standard Error
t Stat
P-value
Lower 95%
Upper 95%
Intercept
-2010.5068
3349.105517
-0.7777
0.44304505
-9454.286633
4245.093122
Size(Sq Ft)
25.0017135
3.193582115
7.729475
1.5961E-08
18.15310465
31.21632226
Regression equation
Rent = 25.0017135*size - 2010.5068
2. Interpret the meaning of b0 and b1 in this problem.
b0 = -2010.5068
when size of the place is 0, the rent is -2010.5068.
But in this problem, range of the data , is 740 to 1,260 Square feet, the interpretation of b0 is meaningless.
b1 = 25.0017135
when there is one square feet increase in size, there is increase of rent by $25.0017135
| Coefficients | Standard Error | t Stat | P-value | Lower 95% | Upper 95% | |
| Intercept | -2010.5068 | 3349.105517 | -0.7777 | 0.44304505 | -9454.286633 | 4245.093122 |
| Size(Sq Ft) | 25.0017135 | 3.193582115 | 7.729475 | 1.5961E-08 | 18.15310465 | 31.21632226 |
