This is a classic econometrics questions and answers Gujarati topic. You cannot compare the $R^2$ of a linear model ($Y = \beta_1 + \beta_2 X$) with a log-log model ($\ln Y = \alpha_1 + \alpha_2 \ln X$) because the dependent variables differ.
Simple regression analysis involves only one independent variable, whereas multiple regression analysis involves more than one independent variable. Multiple regression analysis is used to analyze the relationship between a dependent variable and several independent variables. econometrics questions and answers gujarati
The dummy variable trap occurs when you include a dummy for every category and an intercept term. This causes perfect multicollinearity. This is a classic econometrics questions and answers
A deterministic relationship (e.g., Newton’s law: Force = Mass × Acceleration) implies an exact, functional relationship with no error term. A statistical relationship (e.g., consumption = f(income) + error) involves a stochastic or random disturbance term. As Gujarati emphasizes, economic data is rarely deterministic due to omitted variables, measurement error, or inherent human randomness. Multiple regression analysis is used to analyze the
[ \ln(Y_i) = \beta_1 + \beta_2 \ln(X_i) + u_i ]
Gujarati stresses that OLS is not the only unbiased estimator, but it is the most efficient (narrowest sampling distribution).