Question

what is regression analysis?what are the major challenges associated with the use of regression analysis to estimate the demand for a firm.

Answer 1

Regression analysis is a powerful statistical method that allows you to examine the relationship between two or more variables of interest. It examines the influence of one or more independent variables on a dependent variable.

The major challenges associated with the use of regression analysis are:

MULTICOLLINEARITY

     Multicollinearity refers to the case in which two or more explanatory variables in the regression model are highly correlated, making it difficult or impossible to isolate their individual effects on the dependent variable. With multicollinearity, the estimated OLS coefficients may be statistically insignificant (and even have the wrong sign) even though R² may be "high".

HETEROSKEDASTICITY

     If the OLS assumption that the variance of the error term is constant for all values of the independent variables does not hold, we face the problem of heteroskedasticity. This leads to unbiased but inefficient (ie, larger than minimum variance) estimates of the standard errors (and thus, incorrect statistical tests confidence intervals).

AUTOCORRELATION

    When the error term in one time period is positively correlated with the error term in the previous time period, we face the problem of (positive first-order) autocorrelation. This is common in time-series analysis and leads to downward-biased standard errors (and, thus, to incorrect statistical tests and confidence intervals).

ERRORS IN VARIABLES

    Errors in variables refer to the case in which the variables in the regression model include measurement errors. Measurement errors in the dependent variable are incorporated into the disturbance term and do not create any special problem. However, errors in the explanatory variables lead to biased and inconsistent parameter estimates.