The scatterplot below displays a set of bivariate data along with its least-squaresregression line.400300200100120406080Consider removing the outlier (95,120) and calculating a new least-squares regressionline. What effect(s) would removing the outlier have?a) The coefficient of determination (r2) would increase.b) The correlation coefficient (r) would get closer to 1. TRUEc) The y-intercept of the least-squares regression line would increase.TRUETRUEFALSEFALSEFALSE

It is required to determine whether the coefficient of determination (r2) would increase, correlation coefficient (r) would increase, and the y-intercept of the least-squares regression line would increase, if the outlier (95, 120) is removed to construct a new least-squares regression line.a.The coefficient of determination (r2) gives the proportion of percentage of variation in the response variable that is explained by the fitted model.All points in the dataset except for the outlier (95, 120) lie quite close to the least-squares regression line fitted to the original dataset (the dataset including the outlier), even though the outlier pulls the fitted line towards itself. If the outlier is removed, there would be no such pulling effect. A least-squares regression line fitted to the dataset after removing the outlier will need to fit only the other points, which are already present quite close to each other and form a naturally linear pattern. This new regression line would provide a better fit to the dataset excluding the outlier, than the previous regression line fitted the original dataset including the outlier.Thus, the coefficient of determination (r2) would increase if the outlier (95, 120) is removed to construct a new least-squares regression line. The statement is true.b.The correlation coefficient (r) measures the strength and direction of the association between two numeric variables. The sign of r will be positive for a linear relationship with a positive slope, while the sign of r will be negative for a linear relationship with a negative slope. The magnitude will be closer to 1 for a stronger linear relationship, with 1 indicating a perfect linear relationship, while the magnitude will be closer to 0 for a weaker linear relationship, with 0 indicating a perfect non-linear relationship or no relationship.The points other than the outlier (95, 120) form a tight linear pattern among themselves, with no curvature. The outlier lies far away from the other points and disrupts the naturally occurring linear pattern in the rest of the dataset, which would suggest a moderate to low magnitude of r. If the outlier is removed and a new regression line is fitted to the rest of the data, the linear pattern in these values would be strong, and there would be no point disrupting the linear pattern. In that case, the new straight line would fit the remaining points very well, resulting in a very strong linear relationship, so that the correlation coefficient would become closer to 1.Thus, the correlation coefficient (r) would increase if the outlier (95, 120) is removed to construct a new least-squares regression line. The statement is true.c.The y-intercept is the point at which the regression line intersects the vertical axis.All points in the dataset except for the outlier are such that, higher values of y (vertical axis) are associated with higher values of x (horizontal axis). The outlier (95, 120) is unusual in the sense that it has a comparatively lower value of y for a comparatively higher value of x, when compared to the other points in the dataset. The outlier pulls the line towards itself, that is, it pulls the line vertically downward due to its low y-value corresponding to the higher x-values, which results in the line moving upward corresponding to the lower x-values, similar to the effect of a seesaw. As a result, the dataset with the outlier has a higher y-intercept. When the outlier is removed, there is no such pulling effect working downward corresponding to the higher x-values, so that the line does not move up corresponding to the lower x-values. As a result, after removing the outlier, the position at which the line intersects the vertical axis goes down, so that the y-intercept decreases.Thus, the y-intercept would decrease if the outlier (95, 120) is removed to construct a new least-squares regression line. The statement is false.a. The statement regarding the coefficient of determination (r2) is TRUE.b. The statement regarding the correlation coefficient (r) is TRUE.c. The statement regarding the y-intercept is FALSE.