QuestionHow can I give you the dataset homework needed?Download the data fileRateprof.csv from Canvas. The variables we will use arequality and clarityof a professor or their class. Both variables are ratings made by students on the scale of 1 to 5, with 1 being the worst, and 5 the best.Create a scatterplot withclarity on the horizontal axis andquality on the vertical axis.What is the fitted model? Please provide the equation and pay attention to the notation.Which observation(s), if any, is(are) outlier(s)? Please use -4 and 4 as the thresholds (instead of -2 and 2) for the standardized residuals because the sample size is large.Hint: you may want to use therstandard()function in R.Verify your results on one observation from Part c using the outlier formula presented in class. If you have no outliers, then select the first observation in the data set and verify its standardized residual using formulas presented in the lecture.Which observation(s), if any, is(are) exhibit high leverage? Please use as a guide for identifying large values. Hint: you may want to use thehatvalues()function in R.Verify your results on one observation from Part e using the leverage formula presented in class. If you have not identified any observations as high leverage points, then select the first observation in the data set and verify its leverage value using formulas presented in the lectureWhich observation(s) has the largest Cook’s Distance? Is this observation an influential point? Please use 1 as the threshold for the Cook’s Distance. Hint: you may want to use thecooks.distance()function in R.Verify your results on one point from Part g using the formula for Cook’s distance presented in class. If you have not identified any observations as an influential point, then select the first observation in the data set and verify its Cook’s distance value using formulas presented in the lecture.Let’s remove the outlier(s) you identified in Part c. and refit the model. What is the fitted model? Compare the coefficients in the new model to those in the fitted model in Part b. How different are they? Explain your answer.MathStatistics and Probability STAT 3032
