Margin Of Error Regression Slope
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Linear Regression Confidence Interval Excel
reviews Glossary AP practice exam Problems and solutions Formulas Notation Share with Friends Regression Slope: Confidence Interval This lesson describes how to construct a confidence interval around
Standard Error Of The Slope
the slope of a regression line. We focus on the equation for simple linear regression, which is: ŷ = b0 + b1x where b0 is a constant, b1 is the slope (also called the regression coefficient), x is the value of the independent variable, and ŷ is the predicted value of the dependent variable. Estimation Requirements linear regression confidence interval formula The approach described in this lesson is valid whenever the standard requirements for simple linear regression are met. The dependent variable Y has a linear relationship to the independent variable X. For each value of X, the probability distribution of Y has the same standard deviation σ. For any given value of X, The Y values are independent. The Y values are roughly normally distributed (i.e., symmetric and unimodal). A little skewness is ok if the sample size is large. Previously, we described how to verify that regression requirements are met. The Variability of the Slope Estimate To construct a confidence interval for the slope of the regression line, we need to know the standard error of the sampling distribution of the slope. Many statistical software packages and some graphing calculators provide the standard error of the slope as a regression analysis output. The table below shows hypothetical output for the following regression equation: y = 76 + 35x . Predictor Coef SE Coef
Επιλέξτε τη γλώσσα σας. Κλείσιμο Μάθετε περισσότερα View this message in English Το YouTube εμφανίζεται στα Ελληνικά. Μπορείτε να αλλάξετε slope coefficient formula αυτή την προτίμηση παρακάτω. Learn more slope coefficient definition You're viewing YouTube in Greek. You can change this preference regression slope formula below. Κλείσιμο Ναι, θέλω να τη κρατήσω Αναίρεση Κλείσιμο Αυτό το βίντεο δεν είναι διαθέσιμο. Ουρά παρακολούθησηςΟυράΟυρά http://stattrek.com/regression/slope-confidence-interval.aspx?Tutorial=AP παρακολούθησηςΟυρά Κατάργηση όλωνΑποσύνδεση Φόρτωση... Ουρά παρακολούθησης Ουρά __count__/__total__ AP Statistics: Confidence Intervals for the Slope of a Regression Line Michael Porinchak ΕγγραφήΕγγραφήκατεΚατάργηση εγγραφής2.7752 χιλ. Φόρτωση... Φόρτωση... Σε λειτουργία... Προσθήκη σε... Θέλετε να το δείτε ξανά https://www.youtube.com/watch?v=sMhzfmuGK7I αργότερα; Συνδεθείτε για να προσθέσετε το βίντεο σε playlist. Σύνδεση Κοινή χρήση Περισσότερα Αναφορά Θέλετε να αναφέρετε το βίντεο; Συνδεθείτε για να αναφέρετε ακατάλληλο περιεχόμενο. Σύνδεση Μεταγραφή Στατιστικά στοιχεία 10.965 προβολές 39 Σας αρέσει αυτό το βίντεο; Συνδεθείτε για να μετρήσει η άποψή σας. Σύνδεση 40 4 Δεν σας αρέσει αυτό το βίντεο; Συνδεθείτε για να μετρήσει η άποψή σας. Σύνδεση 5 Φόρτωση... Φόρτωση... Μεταγραφή Δεν ήταν δυνατή η φόρτωση της διαδραστικής μεταγραφής. Φόρτωση... Φόρτωση... Η δυνατότητα αξιολόγησης είναι διαθέσιμη όταν το βίντεο είναι ενοικιασμένο. Αυτή η λειτουργία δεν είναι διαθέσιμη αυτήν τη στιγμή. Δοκιμάστε ξανά αργότερα. Δημοσιεύτηκε στ
the form ŷ=b0+b1x. This page shows how to estimate or test the slope of the regression line, and also how to predict the response value for a particular x. Seealso: An Excel workbook (28KB) is provided to help with calculations. A downloadable TI-83/84 program, MATH200B part7, is provided to compute all these confidence http://brownmath.com/stat/infregr.htm intervals and the prediction interval. Contents: Sampling Distribution Review: Regression on a Sample Regression on a Population Requirements Standard Errors Sampling Distribution for the Slope The Example Requirements Check Confidence Interval for Slope of the Regression Line Hypothesis Test for Slope of the Regression Line Confidence Interval for y Intercept of Regression Line Confidence Interval for Mean Response to a Particular x Prediction Interval for Responses to a Particular x What's New Sampling Distribution Advice: This section confidence interval is rather heavy going. While it's nice to understand the background, you don't actually need it to do the calculations. Especially on a first reading, you might want to skip down to the example. Review: Regression on a Sample Earlier in your course, you learned to find the least-squares regression line that best fits a set of points. (If you need a refresher, see Linked Variables.) That can be done by hand with formulas, or with much saving linear regression confidence of labor by a TI calculator. The line of best fit for a sample has a slope and a yintercept, and it can be written in the form ŷ=ax+b, ŷ=b0+b1x, or similar. Because the correlation is almost never exactly ±1, your data points don't fall exactly on the regression line. For a particular data point (xj,yj) the difference between the prediction and the actual y value is called the residual: ej=yj−ŷj. Another way to look at it is that the actual Y value involves both the prediction from the regression line, and the residual ej that is the discrepancy between the regression line and the actual data point. Symbolically, yj=b0+b1xj+ej. (Don't let the notation confuse you. A number subscript refers to properties of the whole sample, and a letter subscript refers to properties of a particular point. Here the point (xj,yj) includes the residual ej, and you know that the residuals of different points will be different. The slope b0 and intercept b1 are properties of the whole sample because they describe the regression line that was derived from the whole sample.) Because it's quite common to have multiple points in your sample with the same xj and different yj's, a given xj can have more than one residual ej. Naturally, if you take another random sample you expect to get a slightly different regression line. In other words, the
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