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 of the following statements about a linear regression model are correct?i) It is possible that a high R-square can result from outliersii) It is always true that the high the R-square, the better the linear regression model iii) Scatterplot can be helpful in identifying the existence of outliers in fitting a regression modeliv) Regression model cannot produce a range of predictions. v) A p-value higher than 0.5 suggests the estimated coefficient is statistically significant. Question 2Answera.i) and v)b.None of the abovec.i) and iii)d.iv) and v)e.i), ii) and iii)

In simple linear regression, if the value of the correlation coefficient (r) is close to 1 or -1, what can we infer?A) The independent variable has no effect on the dependent variable.B) There is a weak linear relationship between the independent and dependent variables.C) The relationship between the variables is likely non-linear.D) There is a strong linear relationship between the independent and dependent variables.

When conducting a regression analysis, what does the coefficient of determination (R-squared) represent?  A. The strength of the relationship between variables  B. The predicted values of the dependent variable  C. The slope of the regression line  D. The proportion of variance in the dependent variable explained by the independent variable

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.

A simple linear regression model was fitted to two variables: Y, the response variable and X, the explanatory variable.A scatter plot of Y versus X as well as the residual plot after fitting the least squares regression line to the data are given below.Which ONE of the following statements regarding the assumptions for this simple linear regression is FALSE?Group of answer choicesThere are two outliers from the general trend.TThe observation with the largest value of x is likely to have a large effect on the position of the fitted line.Two of the observations have unusual y values given their x values.Two of the observations are outliers in x.There are doubts about the Normality of the errors due to the presence of one or more outliers.