Question

The following data gives the selling price, square footage, number of bedrooms, and age (in years) of condominiums that were sold in a neighborhood in the Bronx in the past six months

           

Selling Price	Square Footage	No. of Bedrooms	Age of Condo
64000	1670	2	30
59000	1339	2	25
61500	1712	3	30
79000	1840	3	40
87500	2300	3	18
92500	2234	3	30
95000	2311	3	19
113000	2377	3	7
115000	2736	4	10
138000	2500	3	1
142500	2500	4	3
144000	2479	3	3
145000	2400	3	1
147500	3124	4	0
144000	2500	3	2
155500	4062	4	10
165000	2854	3	3

1. State the appropriate hypotheses to be tested   

2. Use Excel to run the appropriate regression test

3. Write the regression model equation:

Answer:   _______________________________________________

4. What is the strength of the relationship (strong, weak, moderate, no relationship)?

_______________________ Why? __________________________________

_______________________________________________________________

5. Using your equation from part c, predict the price of a Coop Apartment with 2640 square feet, 2 bedrooms, and is 2 years old.

Answer:   ___________________

6. Interpret b₃ in your equation in part c)        ______________________________________

___________________________________________________________________________

                         ____________________________________________________________________________

Answer 1

Hypothesis Setting:

Null Hypothesis, Ho: The Model does not adequately fits the data i.e. the Model is not a good fit i.e.

  

Alternative Hypothesis, Ha: The Model adequately fits the data i.e, the Model is a good fit i.e.

   for at least one i

We are running F-Test (ANOVA) to test the above hypothesis:

Excel Output:

Test Statistics: Under Ho,

  

where k = 4: No. of Parameters and n = 17 : No. of Observations

Using Excel Output, F = 33.72406 and p-value = 2.12163E-06

Decision Rule: Reject the Null Hypothesis if p-value <

Conclusion: Since, p-value < 0.05 so we reject Ho at 5% level of significance and conclude that the Model is a good fit.

Regression Model Equation is given as:

Strength of the Model:

The model is strong since R2, the coefficient of determination = 0.8861 = 88.61% which means that the model is able to explain 88.61% of the total variation in the Selling Prices.

Prediction:

For X1 = 2640, X2 = 2 and X3 = 2 , the estimated selling price is given as:

Interpretation of coefficient corresponding to Age:

For every one year increase in the age of condominiums, the average selling price is expected to decrease by $1711.54

Excel Steps:

1. Go to Data - Data Analysis - Regression

2. Enter the range of Y variable

3. Enter the range of X variables.

4. Enter where you want the output to be printed.

5. Ok

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