Question

In: Statistics and Probability

PLEASE CLEARLY STATE AND ANSWER EACH QUESTION ( 1THROUGH 6) The following data gives the selling...

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

  1. State the appropriate hypotheses to be tested (6 pts.)
  2. Use Excel to run the appropriate regression test (ATATCH) (6 pts.)
  3. Write the regression model equation: (6 pts.) Answer: _______________________________________________
  4. What is the strength of the relationship (strong, weak, moderate, no relationship)? (4 pts)_______________________ AND 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.
  6. Interpret b3 in your equation in part c)

Solutions

Expert Solution

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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