a)What are the dangers of estimating a model without an intercept?
Qg= 150.83–0.75Pg+ 0.37Po+0.65Y.
(0.04)(0.23)(0.02)(0.52)R-square=0.78
b)What can we conclude about the intercept of the model i.e.,can we say that the
intercept is important in this model in a statistical sense?
a) The dangers of estimating a model without an intercept include the potential for biased estimates of the coefficients, as well as the potential for incorrect inferences about the relationships between the variables. Without an intercept, the model assumes that the dependent variable is zero when all of the independent variables are zero, which may not be the case in reality. Additionally, the model may be misspecified, leading to incorrect inferences about the relationships between the variables.
b) We cannot conclude that the intercept is important in this model in a statistical sense. The R-squared value of 0.78 indicates that the model explains 78% of the variation in the dependent variable, but does not provide any information about the importance of the intercept. To determine the importance of the intercept, we would need to compare the model with and without the intercept and assess the difference in the R-squared values.