Compute Standard Error Regression Slope
Contents |
test AP formulas FAQ AP study guides AP calculators Binomial Chi-square f Dist Hypergeometric Multinomial Negative binomial Normal Poisson t Dist Random numbers Probability Bayes rule Combinations/permutations Factorial Event counter Wizard Graphing Scientific
Standard Error Of Regression Slope Excel
Financial Calculator books AP calculator review Statistics AP study guides Probability Survey sampling standard error of regression slope calculator Excel Graphing calculators Book reviews Glossary AP practice exam Problems and solutions Formulas Notation Share with Friends Regression Slope:
Standard Error Of Regression Slope Formula
Confidence Interval This lesson describes how to construct a confidence interval around the slope of a regression line. We focus on the equation for simple linear regression, which is: ŷ = b0 + how to calculate standard error of regression coefficient 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 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. standard error regression equation 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 T P Constant 76 30 2.53 0.01 X 35 20 1.75 0.04 In the output above, the standard error of the slope (shaded in gray) is equal to 20. In this example, the standard error is referred to as "SE Coeff". However, other software packages might use a different label for the standard error. It might be "StDev", "SE", "Std Dev", or something else.
1: descriptive analysis · Beer sales vs. price, part 2: fitting a simple model · Beer sales vs. price, part 3: transformations of variables · Beer
Standard Error Of Regression Coefficient In R
sales vs. price, part 4: additional predictors · NC natural gas standard error of regression coefficient definition consumption vs. temperature What to look for in regression output What's a good value for R-squared? What's
Standard Error Of Regression Coefficient Matlab
the bottom line? How to compare models Testing the assumptions of linear regression Additional notes on regression analysis Stepwise and all-possible-regressions Excel file with simple regression formulas Excel http://stattrek.com/regression/slope-confidence-interval.aspx?Tutorial=AP file with regression formulas in matrix form If you are a PC Excel user, you must check this out: RegressIt: free Excel add-in for linear regression and multivariate data analysis Mathematics of simple regression Review of the mean model Formulas for the slope and intercept of a simple regression model Formulas for R-squared and standard error http://people.duke.edu/~rnau/mathreg.htm of the regression Formulas for standard errors and confidence limits for means and forecasts Take-aways Review of the mean model To set the stage for discussing the formulas used to fit a simple (one-variable) regression model, let′s briefly review the formulas for the mean model, which can be considered as a constant-only (zero-variable) regression model. You can use regression software to fit this model and produce all of the standard table and chart output by merely not selecting any independent variables. R-squared will be zero in this case, because the mean model does not explain any of the variance in the dependent variable: it merely measures it. The forecasting equation of the mean model is: ...where b0 is the sample mean: The sample mean has the (non-obvious) property that it is the value around which the mean squared deviation of the data is minimized, and the same least-squares criterion will be used later to estimate the "mean effect" of an independent variable. The error that
Tour Start here for a quick overview of the site Help Center Detailed answers to any questions you might http://stats.stackexchange.com/questions/91750/how-is-the-formula-for-the-standard-error-of-the-slope-in-linear-regression-deri have Meta Discuss the workings and policies of this site About Us Learn more about Stack Overflow the company Business Learn more about hiring developers or posting http://www.chem.utoronto.ca/coursenotes/analsci/stats/ErrRegr.html ads with us Cross Validated Questions Tags Users Badges Unanswered Ask Question _ Cross Validated is a question and answer site for people interested in statistics, machine learning, standard error data analysis, data mining, and data visualization. Join them; it only takes a minute: Sign up Here's how it works: Anybody can ask a question Anybody can answer The best answers are voted up and rise to the top How is the formula for the Standard error of the slope in linear regression derived? [duplicate] up standard error of vote 3 down vote favorite This question already has an answer here: Derive Variance of regression coefficient in simple linear regression 2 answers As stated in many textbooks, the Standard error of the slope in linear regression with one variable is $\sqrt{\frac{s^2}{SSX}}$ or some rewrite, ${s^2}$ being the error variance and ${SSX}$ being the sum of the ${x}$-squares. Can anybody help with an explicit proof? regression standard-error share|improve this question edited Apr 14 '14 at 7:05 asked Mar 28 '14 at 20:11 user3451767 11319 marked as duplicate by gung, Nick Stauner, Momo, COOLSerdash, Glen_b♦ Mar 29 '14 at 8:00 This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question. 1 see stats.stackexchange.com/questions/88461/… –TooTone Mar 28 '14 at 23:19 It's reasonably straightforward if you start from the fact that the line goes through $(\bar x,\bar y)$ and write the slope estimator as a kind of average. –Glen_b♦ M
treated statistically in terms of the mean and standard deviation. The same phenomenon applies to each measurement taken in the course of constructing a calibration curve, causing a variation in the slope and intercept of the calculated regression line. This can be reduced - though never completely eliminated - by making replicate measurements for each standard. Multiple calibrations with single values compared to the mean of all three trials. Note how all the regression lines pass close to the centroid of the data. Even with this precaution, we still need some way of estimating the likely error (or uncertainty) in the slope and intercept, and the corresponding uncertainty associated with any concentrations determined using the regression line as a calibration function. Tips & links: Skip to uncertainty of the regression Skip to uncertainty of the slope Skip to uncertainty of the intercept Skip to the suggested exercise Skip to Using Excel’s functions Download a specimen Excel file for this section Navigation: Introduction Bibliography Contact Info Copyright How to Use Concept Map Site Map Excel™ Basics Entering Data Formulas Plotting Functions Trendlines Basic Statistics Stats in Anal Chem Mean and Variance Error and Residuals Probability Confidence Levels Degrees of Freedom Linear Regression Calibration Correlation Linear Portions Regression Equation Regression Errors Using the Calibration Limits of Detection Outliers in Regression Evaluation & Comparison Hypotheses t-test 1- and 2-tailed Tests F-test Summary Quick Links: Site Map Concept Map Next Page Previous Page Next Topic Previous Topic The Uncertainty of the Regression: We saw earlier that the spread of the actual calibration points either side of the line of regression of y on x (which we are using as our calibrat