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

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)

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.