In: Statistics and Probability
PLEASE CLEARLY STATE AND ANSWER EACH QUESTION ( 1THROUGH 6)
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 |
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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