Quality of oil is measured in API gravity degrees€“the higher the degrees API, the higher the quality. The table shown below is produced by an expert in the field who

believes that there is a relationship between quality and price per barrel. Oil degrees API 27.0 28.5 30.8 31.3 31.9 34.5 34.0 34.7 37.0 41.0 41.0 38.8 39.3 Price per

barrel (in $) 12.02 12.04 12.32 12.27 12.49 12.70 12.80 13.00 13.00 13.17 13.19 13.22 13.27

1. Predict with 95% confidence the oil price per barrel for an API degree of 35. 2. Estimate with 95% confidence the average oil price per barrel for an API degree of

35. 3. Which interval in the previous two questions is narrower: the confidence interval estimate of the expected value of y or the prediction interval for the same

given value of x (10 years) and same confidence level? Why? 4. Use the regression equation to determine the predicted values of y.

5. Use the predicted values and the actual values of y to calculate the residuals. 6. Plot the residuals against the predicted values . 7. Does it appear that

heteroscedasticity is a problem? Explain.

8. Draw a histogram of the residuals. Does it appear that the errors are normally distributed? Explain. 9. Use the residuals to compute the standardized residuals. 10.

Identify possible outliers.