Use the housing price data in HPRICEl for this exercise. (i)...

Use the housing price data in HPRICEl for this exercise. (i) Estimate the model $\log ($price$)=\beta_{0}+\beta_{1} \log ($lotsize$)+\beta_{2} \log (s q r f t)+\beta_{3} b d r m s+u$ and report the results in the usual OL.S format. (ii) Find the predicted value of log(price), when lotsize $=20,000, s q r f t=2,500,$ and $b d r m s=4$ Using the methods in Section $6-4,$ find the predicted value of price at the same values of the explanatory variables. (iii) For explaining variation in price, decide whether you prefer the model from part (i) or the model price $=\beta_{0}+\beta_{1}$ lotsize $+\beta_{2} s q r f t+\beta_{3} b d r m s+u$

Use the housing price data in HPRICEl for this exercise.
(i) Estimate the model
$\log ($price$)=\beta_{0}+\beta_{1} \log ($lotsize$)+\beta_{2} \log (s q r f t)+\beta_{3} b d r m s+u$
and report the results in the usual OL.S format.
(ii) Find the predicted value of log(price), when lotsize $=20,000, s q r f t=2,500,$ and $b d r m s=4$ Using the methods in Section $6-4,$ find the predicted value of price at the same values of the explanatory variables.
(iii) For explaining variation in price, decide whether you prefer the model from part (i) or the model
price $=\beta_{0}+\beta_{1}$ lotsize $+\beta_{2} s q r f t+\beta_{3} b d r m s+u$

Key Concepts

Ordinary Least Squares (OLS) Regression

OLS regression is a fundamental statistical method used to estimate the parameters of a linear relationship between one dependent variable and one or more independent variables by minimizing the sum of the squared deviations between the observed and predicted values. It provides a framework for estimating the impact of changes in explanatory variables on the outcome of interest.

Log Transformation

A log transformation involves taking the natural logarithm of one or more variables, which can help linearize relationships, reduce heteroskedasticity, and allow for interpretations in terms of percentage changes rather than absolute differences. This is especially useful when the data exhibit exponential growth or multiplicative effects.

Prediction in Regression Models

Prediction in regression involves using the estimated coefficients from a model to compute the expected value of the dependent variable for given values of the independent variables. When the dependent variable has been log-transformed, predictions on the original scale require exponentiation of the predicted values to accurately reflect the outcome in its original units.

Model Specification and Comparison

Model specification refers to choosing the form and variables included in a regression model, which is critical for capturing the true relationship between the dependent and independent variables. Comparing models typically involves checking for goodness-of-fit, interpretability of coefficients, and whether the functional form appropriately captures the underlying data patterns. This helps in determining the most effective model for analysis and prediction.

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