If the predicted value of a linear probability model is 2.5: a. it means that the dependent variable is equal to 1 with certainty. b. the regression R2 is then equal to 0.999. c. the dependent variable observed value must be incorrect. d. this has little interpretation since probability is always bounded between zero and one. e. All of the above. f. None of the above.

In the probit model, a predicted probability value of 0.95 means that: a. the most likely value the dependent variable will take on is 1.  b. given the values for the explanatory variables, there is a 95 percent probability that the dependent variable will equal one. c. given the values for the explanatory variables, there is a 5 percent probability that the dependent variable will equal zero. d. given the values for the explanatory variables, it is unlikely that the dependent variable will equal zero. e. All of the above. f. None of the above.

If you run a simple linear regression and the output indicates a very small p-value for the slope coefficient and a high value for the R-squared statistic, which of the following conclusions is most appropriate?A) The independent variable has no meaningful relationship with the dependent variable.B) The relationship between the independent and dependent variables is likely coincidental.C) The model explains a significant proportion of the variance in the dependent variable, and the relationship is likely not due to chance.D) There is a high likelihood of overfitting in the model.

Which two of the of the following statements are correct regarding R2 as a tool to evaluate a regression model. Multiple answers allowed.a.The R2 is the proportion of the total variation in X that can be explained by the variation in the dependent variable in the model.b. If the R2 value is greater than 1, then it shows that the regression model is a very good fit.c.The R2 value needs to be reported in presenting regression results as it shows the relative precision of the model for the users to consider.d.R2 reflects the model’s improvement of the predicted value over the estimator of the sample mean (Y-bar).

Question 1: In a regression analysis, what information gives R²?a) The unexplained variance by the predictorsb) The share of the dependent variable variance explained by the predictorsc) The badness of the fitd) The quality of the data selection

If the R-squared (R2) score of a regression model is 0, what does it imply about the model's performance?(1 Point)a) The model has perfect predictions.b) The model has no predictive power.c) The model's predictions are 100% accurate.d) The model has overfit the data