Parametric Statistical Inference/Modelling
1. Create box plots for both X and Y. Are there any outliers
2 Make a Scatter plot with Regression. Does there appear to be a linear relationship? What two points appear to be potential outliers?
3. Check for outliers using the semi-studentized method. Are there any outliers? What are the absolute values of the semi-studentized residuals you identified in question 2?
4. Do a check of normality by using a probability plot of the residuals. Include:
a. The null and alternative hypotheses,
b. The p-value of the test,
c. Your decision based on a 0.05 level of significance, and
d. Minitab copy of your plot.
5 Do a check of equal variances by performing a Modified Levene Test. Include:
a. The null and alternative hypotheses,
b. The p-value of the test,
c. Your decision based on a 0.05 level of significance, and
d. Minitab copy of your plot.
6 Perform a Lack of Fit Test to check if linear regression function is appropriate. Include:
a. The null and alternative hypotheses,
b. The correct F-statistic and p-value of the test,
c. Your decision based on a 0.05 level of significance, and
d. Minitab copy of your ANOVA output.
7. Even though you may not have found any assumption violations perform a Box-Cox analysis on Y to see if any transformation is suggested. Include the
a. Estimated and rounded lambda values,
b. The interpretation of this value, and
c. The Box-Cox plot.
NOTE: This can only be done using Minitab Version 15 or higher – i.e. student version 14 does not contain Box-Cox program.
8. Find Bonferroni joint confidence intervals for Bo and B1 with a 90% family confidence level and include your interpretation of these intervals. You can use the Minitab output to find s{bo} and s{b1}
9. Use Minitab to find Bonferroni simultaneous confidence intervals for new X observations of and 10 using a 95% family confidence level. Include your the output and interpretation of these intervals.
9.1 Follow-up question 1: What is the interpretation of the level of confidence for the confidence intervals in the output?
9.2 Follow-up question 2: Can you think of a reason why these new X values might not be reliable?
9.3 Follow-up question 3: Show mathematically how one would use the Minitab output to get the simultaneous level of confidence for new observations.