Aims

Objectives

The following objectives, together with those of the previous section, will help you to assess how well you have mastered the relevant material. By the end of this section you should be able to:

• State the model assumptions for the simple Normal linear regression model.
• Derive the mean, variance and distribution of the estimators of the slope and intercept of the fitted regression line, and calculate the corresponding standard errors.
• Construct exact confidence intervals for the values of both the slope and the intercept.
• Perform standard hypothesis tests on the values of both the slope and the intercept.
• Use the summary() command in R to calculate confidence intervals and perform hypothesis tests on the values of both the slope and the intercept.
• Identify from an informal problem description situations where a paired t-test or a two sample t-test would be appropriate, and, in the latter case, identify whether or not a pooled two sample t-test would be appropriate.
• State appropriate model assumptions and formulate appropriate null and alternative hypotheses for each of the types of two-sample or paired t-test listed above.
• Identify an appropriate test statistic and its distribution under the null hypothesis for each of the types of two-sample or paired t-test listed above.
• Use the methods of Section 8 (Testing Hypotheses) to compute appropriate p-values or critical regions and report appropriate conclusions for each of the types of two-sample or paired t-test listed above.
• Use appropriate commands in R to perform each of the types of two-sample or paired t-test listed above, and correctly interpret and report the output of the procedures.

Suggested Reading

Handouts and Problem Sheets

Questions - set in week 11

PROBLEM SHEET 10 -- Questions 1, 5, 7, 8

Interesting links