1 – α – confidence coefficient
α (0<α<1) – level of significance
Confidence limits – endpoints of the confidence interval
β2 - - lower confidence limit
β1 - - upper confidence limit
Following aspects of interval estimation:
1. Since β2, although an unknown, is assumed to be some fixed number, either it lies in the interval or it does not.
2. Random interval will vary from one sample to the next because it is based on β2, which is random.
3. Since the confidence interval is random, the probability statements attached to it should be understood in the long-run sense, that is, repeated sampling.
Confidence Intervals for Regression Coefficients β1 and β2
- Confidence Interval for β2
- Confidence Interval for β1
- Confidence Interval for
- Hypothesis Testing: the Confidence-Interval Approach
- Two-sided or Two-tail test
- One-sided or One-tail test
- Testing the significance of Regression Coefficients: the t – Test
In the language of significance tests, a statistic is said to be statistically significant if the value of the test statistic lies in the critical region. In this case the null hypothesis is rejected. By the same token, a test is said to be statistically insignificant if the value of the test statistic lies in the acceptance region.
Testing the Significance of : The r2 Test
Hypothesis Testing: Some Practical Aspects
- The Meaning of “Accepting” or “Rejecting” a Hypothesis
- The “Zero” Null Hypothesis and the “2 – t” Rule of Thumb
- Forming the Null and Alternative Hypotheses
- The Exact Level of Significance: The P Value
Application of Regression Analysis: The Problem of Prediction
- Individual Prediction
Reporting the Results of Regression Analysis
Evaluating the Results of Regression Analysis
- Normality Tests
Normal Probability Plot – comparatively simply graphical device to study the shape of the probability density function of a random variable.
Jacque-Bera Test of Normality – is an asymptotic or large-sample test. It is also based on OLS residuals. This test first computes the skewness and kurtosis.
JB = n S2 + (k – 3)2