![]() Some of the predictors will be significant. It’s so easy to add more variables as you think of them, or just because the data are handy. Together we will use the slope and y-intercept of the least-squares regression to estimate the slope and y-intercept of the population regression line, construct confidence intervals, and use a significance tests for the slope to determine the linear relationship between x and y in the population.Multiple regression can be a beguiling, temptation-filled analysis. And as always, we will ensure that we can calculate the necessary values by hand and with technology. We will work through how to calculate the confidence interval and draw inferences about the true regression line by using raw data as well as summary statistics and computer output data. The standard error of the slope is calculated by dividing the standard deviation of the residuals by the square root of the sum of the squares for x. The critical value, or t-interval, is found using a t-distribution with n-2 degrees of freedom. Then, we will need to determine the margin of error, which is the product of the critical value and the slope’s standard error. Okay, so for confidence intervals, which are sometimes referred to as prediction intervals, we will use the slope of the regression equation as our point estimate. The great thing is that we already know all the steps and procedures for finding confidence intervals and significance tests from our previous units, so this is just an extension of what we already know as outlined by Stat Trek. Once we have established the conditions have been met, we are ready to conduct a confidence interval or a hypothesis test. And Random: The data is produced from a well-designed, random sample or experiment.Equal: The variance of y is the same for all values of x.Normal: For any fixed value of x, the responses of y varies according to a normal distribution.Independent: The individual observations are independent. ![]()
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |