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Produce the summary statistics (the Five-number Summary, Mean, and SD) for x and y. [3 marks]

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Instructions:

Please hand in your HW on paper and in person at the beginning of class on the due date.

Be sure to include your name, student number., and course and section number.

You can do this HW in pairs. If you do so, please hand in one paper with both your names on it.

 

Data was collected from 63 geographical zones in Sweden on auto insurance claims. In particular we want to predict Y = the total auto insurance payout (in thousands of Swedish Krona (kr)) using X = no. of claims.

 

1. Produce the summary statistics (the Five-number Summary, Mean, and SD) for x and y. [3 marks]

 

2. Produce the Scatter Plot of X and Y, along with the Correlation Coefficient. [2 marks]

 

3. Based on the data can we conclude that X and Y are linearly related? Support your answer by referring to the appropriate outputs. [3 marks]

 

4. Note the two observation on the upper right hand corner. Are these observations outliers? Briefly explain your answer. [2 marks]

 

5. Fit the Simple Regression model of Y on X. Report the Least Square Line equation, and the RMSE. R calls it “residual standard error.” [2 marks]

6. One of the observations, the one on row 43 in the Excel file, has x = 60, and y = 202.4. Calculate the residual for this observation and interpret what the number means. [4 marks]

7. Predict the auto insurance payout in a zone with 50 claims. Use an interval using a calculation that would be correct 95% of the time. [2 marks]

8. Produce the Residual Plot and the Density Trace of the Residuals [2 marks]

9. Explain what the Normality assumption means in the context of this problem. And assess whether this assumption seems reasonable in this problem. [4 marks]

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