Consider the following regression model: y = ₀ + ₁x₁ + u. Which of the following is a property of Ordinary Least Square (OLS) estimates of this model and their associated statistics? A)The sum, and therefore the sample average of the OLS residuals, is positive. B)The sum of the OLS residuals is negative. C) The sample covariance between the regressors and the OLS residuals is positive. D) The point ( ) always lies on the OLS regression line.

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The point (11eab06d_252a_899e_beed_d9ed2646e052_TB2133_11) is the sample mean of the dependent variable y and therefore, it always lies on the OLS regression line. Options A, B, and C are incorrect as the OLS residuals do not necessarily sum to zero, may be positive or negative, and may have a sample covariance with regressors that can be positive, negative or zero. An important property of the OLS estimates is that the point ( 11eab06d_252a_b0af_beed_63776a17138f_TB2133_11 ) always lies on the OLS regression line. In other words, if 11eab06d_252a_d7c0_beed_1f1edd3ae512_TB2133_11 , the predicted value of y is 11eab06d_252a_d7c1_beed_71777f64ee59_TB2133_11 .

Consider the Following Regression Model: Y = 0

Consider the Following Regression Model: Y = ₀