Unit 4 : Hypothesis Testing & Confidence Intervals in Simple Linear Regression Flashcards Preview

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When can we say that heteroscedasticity exists?

When the variance of the error terms are not constant.


Why should we not use OLS estimators in heteroscedastic models?

As variance terms are inconsistent, the standard error terms calculated often come out to be too small. The OLS estimators are no longer efficient.


How do we calculate the standard error of heteroscedastic models given OLS estimators are inefficient?

- Use GLS estimators
- Use OLS to estimate model but then deal with standard errors differently. (ALWAYS use heteroscedastic-robust standard errors in these models).


What is a confidence interval?

This is a range of values that we are certain that the true data values lie in.


What is hypothesis testing?

This is when we propose a question of whether one variable will affect the other. It uses the information that we have about a population to try and estimate the relationship in a sample size.


What is the null hypothesis?

A specific estimate of the value of the regression parameter.
This differs from the alternative hypothesis which is just another specific estimate - if B1 value is less than null, then left-tailed. The inverse is true.

If B1 is just shown as not equal to null, then there are two sides alternative hypothesis.


What can we use to determine if we should accept or reject the null hypothesis?

We should use the test statistic. If alternative hypothesis is true, then test statistic will be very large or very small. (range of values is called the rejection region).

One-sided test and both sided tests can be used. This i when null hypothesis is found to be greater than or less than t statistic.


What does the p-value tell us?

This tells us the likelihood of an observed data point happening by chance - the lower the p-value, the likelier it is for the alternative hypothesis to hold true.

Therefore, if the p value is less than the significance level (a), then the null hypothesis should be rejected. The inverse is true.

To calculate p value of a two sided graph, multiply p value by 2.


What is the significance level?

This is the probability of rejecting the null hypothesis when it is true. A significance level of 0.05 indicates that there is a 5% probability that a different value


What are the critical regions?

These are the areas of the graph (sample mean) that could be found (usually with low %).
When a null hypothesis is rejected, that value does not fall within the critical region(s).


What does it mean for a data set to be statistically significant?

The null hypothesis will hypothesise that data results occur due to chance alone. To disprove this, we look at alternative hypotheses and prove that the p value is less than significance level (hence disproving null hypothesis), also telling us that the data set is not because of chance.