The Rent in the sample range from $15,500 to $32,000 and the office sizes in the

ID: 3429968 • Letter: T

Question

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

ANOVA

Significance F

Regression

553051465.6

5.53E+08

59.7447854

1.59606E-08

Residual

268450081.2

9256899

Total

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

ANOVA

Significance F

Regression

553051465.6

5.53E+08

59.7447854

1.59606E-08

Residual

268450081.2

9256899

Total

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

Explanation / Answer

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