Further statistics 2

1. LINEAR REGRESSION

1.1 Least squares linear regression

1.2 Residuals

1.3 Mixed exercise 1

1.4 Review exercise for chapter 1

 

2. CORRELATION

2.1 The product moment correlation coefficient

2.2 Spearman’s rank correlation coefficient

2.3 Hypothesis testing for zero correlation

2.4 Mixed exercise 2

2.5 Review exercise for chapter 2

 

3. CONTINUOUS DISTRIBUTIONS

3.1 Continuous random variables

3.2 The cumulative distribution function

3.3 Mean and variance of a continuous distribution

3.4 Mode, median, percentiles and skewness

3.5 The continuous uniform distribution

3.6 Modelling with the continuous uniform distribution

3.7 Mixed exercise 3

3.8 Review exercise for chapter 3

 

4. COMBINATIONS OF RANDOM VARIABLES

4.1 Combinations of random variables

4.2 Mixed exercise 4

4.3 Review exercise for chapter 4

 

5. ESTIMATION, CONFIDENCE INTERVALS AND TESTS USING A NORMAL DISTRIBUTION

5.1 Estimators, bias and standard error

5.2 Confidence intervals

5.3 Hypothesis testing for the difference between means

5.4 Use of large sample results for an unknown population

5.5 Mixed exercise 5

5.6 Review exercise for chapter 5

 

6. FURTHER HYPOTHESIS TESTS

6.1 Variance of a normal distribution

6.2 Hypothesis testing for the variance of a normal distribution

6.3 The $F$-distribution

6.4 The $F$-test

6.5 Mixed exercise 6

6.6 Review exercise for chapter 6

 

7. CONFIDENCE INTERVALS AND TESTS USING THE $t$-DISTRIBUTION

7.1 Mean of a normal distribution with unknown variance

7.2 Hypothesis test for the mean of a normal distribution with unknown variance

7.3 The paired $t$-test

7.4 Difference between means of two independent normal distributions

7.5 Hypothesis test for the difference between means

7.6 Mixed exercise 7

7.7 Review exercise for chapter 7

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