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)

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.

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.

2. Discuss Linear Regression with an example.

A scatterplot with a linear model is shown.Which best describes the linear model? A. The linear model does not describe the data well because there are not the same amount of points above the line as below the line. B. The linear model describes the data well because the points are scattered above and below the line. C. The linear model does not describe the data well because it does not go through any of the points. D. The linear model describes the data well because some of the points are close to the line.

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