MA317 (2020/21) 17 MODELLING EXPERIMENTAL DATA
3.3 Problems
Problem 3.1. Example 3.1 continued.
Compute a 95% confidence interval for b.
Problem 3.2. Test about the slope parameter.
Statistical model: (Yi , xi ) for i = 1, . . . , n independent distributed, Yi ∼ N (a + bxi , σ 2 ) and xi ∈ R,
σ > 0, a ∈ R, b ∈ R.
Derive a hypothesis test for the slope parameter b.
Problem 3.3. Example 3.1 continued. Conduct a hypothesis test for the slope parameter b.
Problem 3.4. Recall
Sxy Syy − SSR
r=p , R2 =
Sxx Syy Syy
Show r2 = R2 .
3.3 Problems
Problem 3.1. Example 3.1 continued.
Compute a 95% confidence interval for b.
Problem 3.2. Test about the slope parameter.
Statistical model: (Yi , xi ) for i = 1, . . . , n independent distributed, Yi ∼ N (a + bxi , σ 2 ) and xi ∈ R,
σ > 0, a ∈ R, b ∈ R.
Derive a hypothesis test for the slope parameter b.
Problem 3.3. Example 3.1 continued. Conduct a hypothesis test for the slope parameter b.
Problem 3.4. Recall
Sxy Syy − SSR
r=p , R2 =
Sxx Syy Syy
Show r2 = R2 .
