**Educational Exercise on Regression Analysis****Given data for two variables, \( x \) and \( y \):**\[\begin{array}{|c|c|c|}\hlinex_i & 6 & 11 & 15 & 18 & 20 \\\hliney_i & 6 & 12 & 12 & 20 & 30 \\\hline\end{array}\]### (a) Develop an estimated regression equation for these data. *(Round your numerical values to two decimal places.)*Estimated Regression Equation: \( \hat{y} = \) [Answer will be input by the student]---### (b) Compute the residuals. *(Round your answers to two decimal places.)*Residuals Computation Table:\[\begin{array}{|c|c|c|}\hlinex_i & y_i & \text{Residuals} \\\hline6 & 6 & \\11 & 12 & \\15 & 12 & \\18 & 20 & \\20 & 30 & \\\hline\end{array}\]---### (c) Develop a plot of the residuals against the independent variable \( x \). Do the assumptions about the error terms seem to be satisfied?- The plot suggests a generally horizontal band of residual points indicating that the error term assumptions are satisfied.- The plot suggests curvature or a funnel pattern in the residuals indicating that the error term assumptions are not satisfied.[Answer should be selected based on the plot created by the student]---### (d) Compute the standardized residuals.*(Round your answers to two decimal places.)*Standardized Residuals Table:\[\begin{array}{|c|c|c|}\hlinex_i & y_i & \text{Standardized Residuals} \\\hline6 & 6 & \\11 & 12 & \\15 & 12 & \\18 & 20 & \\20 & 30 & \\\hline\end{array}\]---### (e) Develop a plot of the standardized residuals against \( \hat{y} \). What conclusions can you draw from this plot?- The standardized residual

Given the data of two variables x and y as66119151218202030

Given are data for two variables, x and y. (a) Develop an estimated regression equation for these data. (Round your numerical values to two decimal places.) (b) Compute the residuals. (Round your answers to two decimal places.) X, Y, Residuals 6 6 11 9 x₁ 6 11 15 18 20 Y 6 9 12 20 30 15 12 18 20 30 (c) Develop a plot of the residuals against the independent variable x. Do the assumptions about the error terms seem to be satisfied? O The plot suggests a generally horizontal band of residual points indicating that the error term assumptions are not satisfied. The plot suggests curvature in the residuals indicating that the error term assumptions are not satisfied. The plot suggests curvature in the residuals indicating that the error term assumptions are satisfied. O The plot suggests a funnel pattern in the residuals indicating that the error term assumptions are not satisfied. O The plot suggests a generally horizontal band of residual points indicating that the error term assumptions are satisfied. (d) Compute the standardized residuals. (Round your answers to two decimal places.) 6 20 X, Y, Standardized Residuals 11 18 20 6 15 12 9 20 30 (e) Develop a plot of the standardized residuals against ý. What conclusions can you draw from this plot? The standardized residual plot has the same shape as the original residual plot. The plot suggests a generally horizontal band of residual points indicating that the error term assumptions are not satisfied O The standardized residual plot has a different shape than the original residual plot. The plot suggests a generally horizontal band of residual points indicating that the error term assumptions are satisfied. The standardized residual plot has a different shape than the original residual plot. The plot suggests a funnel pattern in the residuals indicating that the error term assumptions are not satisfied. The standardized residual plot has the same shape as the original residual plot. The plot suggests curvature in the residuals indicating that the error term assumptions are not satisfied. O The standardized residual plot has a different shape than the original residual plot. The plot suggests curvature in the residuals indicating that the error term assumptions are satisfied.