Understanding and Application of Hypothesis Testing, Regression Models, and Logistic Regression

Full Answer Section

     

1. Draft the Model:

Our model will look something like this: Y (Selling Price) = β₀ + β₁X₁ (Square Footage) + β₂X₂ (Number of Bedrooms) + β₃X₃ (Location) + ε Where: * β₀ is the intercept (constant term) * β₁ to β₃ are the regression coefficients for each independent variable * ε is the error term (accounts for unexplained variance)

3. Data Collection:

We need a dataset containing information on selling prices, square footage, number of bedrooms, and location for multiple houses.

4. Model Fitting and Evaluation:

Use statistical software to fit the model to the data. This will estimate the values of the coefficients (β₀, β₁, β₂, β₃).

5. Interpretation:

• The intercept (β₀) represents the predicted selling price when all independent variables are zero (which might not be realistic, but helps interpret the coefficients).
• Each coefficient (β₁) tells you how much the selling price is expected to change, on average, for a one-unit increase in the corresponding independent variable (holding other variables constant).
• We will evaluate the model's goodness-of-fit using metrics like R-squared (proportion of variance explained by the model) and p-values for the coefficients (significance of their impact on the model).

6. Prediction:

Once the model is validated, we can use it to predict the selling price of new houses based on their square footage, number of bedrooms, and location.  

Sample Solution

 

Chapter of Choice: Chapter 13: Simple and Multiple Linear Regression Models

Statistical Problem: We want to predict the selling price of a house based on several factors that might influence it, such as square footage, number of bedrooms, and location.

Draft Strategy using Multiple Linear Regression Model:

1. Define Variables:

   • Dependent Variable (Y): Selling price of the house (numerical)
   • Independent Variables (X):
     • Square footage of the house (numerical)
     • Number of bedrooms (numerical)