Final answer:
The correct statement is B, indicating that if the confidence interval for the regression slope coefficient includes zero, the true population parameter could indeed be zero.
Step-by-step explanation:
The true statement among the options given is B. If the confidence interval estimate for the regression slope coefficient, based on the sample information, crosses over zero, the true population regression slope coefficient could be zero. This implies that there might not be a significant linear relationship between the independent and dependent variables in the population. The confidence interval provides a range of values within which the true population parameter is likely to fall, and if zero is within this range, it indicates that the effect could be nonexistent.
Statement C is not necessarily true because the y-intercept of a multiple regression model can be positive or negative regardless of the signs of the regression slope coefficients. It is contextual and depends on the specific data. Statement D is incorrect because the R-squared value will not be smaller than the adjusted R-squared when adding insignificant variables; in fact, adjusted R-squared takes into account the number of variables relative to the number of observations and adjusts for the inclusion of non-significant predictors, often leading to a lower value than the R-squared when unnecessary variables are included.