muhammadrafiq

1. Suppose f,g : R -> R are continuous on sets Df, Dg C R respectively. Use theoremsfrom class to prove that h(x,y) := f(x) + g(y) is continuous on Df Dg. 2. Let f(x, y) =( x^2 ycos(y)^2) /(x^2 + 1/2y^2). It can be shown that lim(x,y)->(0,0) f(x, y) = 0.(a) Let = 0.1. Use algebra to find a > 0 satisfying the formal denition of thelimit. (You will get extra credit if you can nd a general formula for in termsof , but it is not necessary.)

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 answer all questions.

The sample mean of the dependent and independent variables satisfy the estimated OLS sample regression line.

No perfect multicollinearity among explanatory variables.

The conditional variance of the dependent variable on the explanatory variables is constant.

Standard error of the regression is used to estimate the standard errors of the corresponding OLS regressors.

Perfect collinearity between explanatory variables.

Mean conditional independence of the error term.

Error term conditional on the explanatory variables of the regression model is normally distributed.

The zero conditional expectation of the error term on the explanatory variables.

The zero correlation between the fitted values and the residuals of a multiple regression model.

A random sample of the dependent and explanatory variables of a regression model is available.

1. Assumption of the classical linear regression model.
2. Not an assumption of the classical linear regression model.