Final answer:
The least squares assumption e(uixi)=0 implies that the expected value of the residuals times the independent variable is zero. Hence, statement A. e(yixi)=b0 + b1xi is correct.
Step-by-step explanation:
The least squares assumption e(uixi)=0 pertains to the linear regression models and implies that the expected value of the residuals (errors) ui multiplied by xi is zero. This assumption is essential for ensuring that the best-fitting line is unbiased and that the estimates of the slope and intercept are accurate.
The correct statement implied by this assumption is A. e(yixi)=b0 + b1xi, where y is the dependent variable, x is the independent variable, b0 is the intercept, and b1 is the slope of the regression line. The assumption means that on average, the product of the residuals and the independent variable is zero.
This does not directly say anything about the expected value of yi being zero or equal to the linear model itself, nor does it imply an estimation of a particular value for yi given xi. Instead, it indicates that the linear model has no systematic errors that correlate with x values.