Estimations, Hypothesis Testing and Regression Flashcards
How do you use the likelihood function?
After identifying the correct formula and applying it, take the natural log on both sides for easier differentiation. When you differentiate, make it equal to zero. Rearrange to find the value of the estimate. If there is a uniform distribution of data (each outcome is equally likely) then L is equal to the function by the power of n and aim for the biggest value.
How do you use the confidence interval?
The confidence interval can help find the critical value. To find the number that corresponds to the correct critical value on the appropriate graph, take 1 - the confidence interval and divide by 2. If the data follows a normal distribution (large sample size and population variance is known) take 1 - the value you worked out. This value is the result of a Z value so you can trace back to it. Times this Z value by the standard error and the confidence interval is the mean ± the final value worked out. If sample size is small and population variance is unknown, there is t-distribution. To use the t-distribution graph, use n-1 and half of 100 - confidence interval (using percentages).
How do you use the confidence interval for mean and variance?
Using the confidence interval for the mean works in the exact same way as regular C.I questions. For variance you need to use the x2 graph in the same way as you would for a t distribution. The equation is given so consider the term with 1 - alpha in it. In the case of a 95% CI, this term would suggest an xn;0.975 term which is read off the graph as 97.5.
How do you use one-tailed and two-tailed test hypthesis?
The significance level given is 1 - confidence interval. If you are looking for a result that is different from the average value you should go with a two-tailed hypothesis. If you are looking for a value significantly higher or lower than the average then go with one tailed (note that for a 95% CI, you look for 5% instead of 2.5% because of the one-tailed graph). In both cases, there is a null hypothesis that is always equal to the average. If there is a t-distribution, use (the calculated mean minus the estimated mean divided by the standard error). If there is an x2-distribution, use ( (n-1) multiplied by the calculated (s.d)2 divided by the estimated (s.d)2). If the critical value is smaller than the (absolute) hypothesis value then the null hypothesis is rejected (except when you anticipated a lower than average hypothesis value). For a Z test (two means) use the formula (rearranged). For an F test (two variances) use the formula (basically the variance of one divided by the variance of the other).
What is the formula of the regression line? Also how do you find the value of the residual?
y = α + βx
(x and y terms being the means)
(K can be used instead of y)
To work out the value of the residual, sub the value of x in the equation. Round up the result you get and minus it from the unrounded result.
