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.