How To Calculate Standard Error Of The Slope In Excel
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Du siehst YouTube auf Deutsch. Du kannst diese Einstellung unten ändern. Learn more You're viewing YouTube in German. You can change this preference below. Schließen Ja, ich möchte sie behalten Rückgängig machen Schließen Dieses Video ist error in slope excel nicht verfügbar. WiedergabelisteWarteschlangeWiedergabelisteWarteschlange Alle entfernenBeenden Wird geladen... Wiedergabeliste Warteschlange __count__/__total__ How to how to calculate error in slope calculate the error in a slope using excel Maxamus AbonnierenAbonniertAbo beenden6363 Wird geladen... Wird geladen... Wird verarbeitet... Hinzufügen standard deviation of slope formula Möchtest du dieses Video später noch einmal ansehen? Wenn du bei YouTube angemeldet bist, kannst du dieses Video zu einer Playlist hinzufügen. Anmelden Teilen Mehr Melden Möchtest du dieses Video
How To Calculate Standard Error Of Slope And Intercept
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in Excel (Linear Regression in Physics Lab) January 4, 2013 by Jeff Finding Standard Error of Slope and Y-Intercept using LINEST in Excel (Linear Regression in Physics Lab) In Excel, you can apply a line-of-best fit to any scatterplot. The equation for the fit can be displayed but the standard error of the slope and formula for calculating error in slope y-intercept are not give. To find these statistics, use the LINEST function instead. The LINEST function
How To Find Standard Deviation Of Slope And Intercept
performs linear regression calculations and is an array function, which means that it returns more than one value. Let's do an example to see how
Uncertainty In Slope Of Best Fit Line
it works. Let's say you did an experiment to measure the spring constant of a spring. You systematically varied the force exerted on the spring (F) and measured the amount the spring stretched (s). Hooke's law states the F=-ks (let's ignore https://www.youtube.com/watch?v=eV-RKGGrtA8 the negative sign since it only tells us that the direction of F is opposite the direction of s). Because linear regression aims to minimize the total squared error in the vertical direction, it assumes that all of the error is in the y-variable. Let's assume that since you control the force used, there is no error in this quantity. That makes F the independent value and it should be plotted on the x-axis. Therefore, s is the dependent variable and should be http://www.fiz-ix.com/2013/01/finding-standard-error-of-slope-and-y-intercept-using-linest-in-excel-linear-regression-in-physics-lab/ plotted on the y-axis. Notice that the slope of the fit will be equal to 1/k and we expect the y-intercept to be zero. (As an aside, in physics we would rarely force the y-intercept to be zero in the fit even if we expect it to be zero because if the y-intercept is not zero, it may reveal a systematic error in our experiment.) The images below and the following text summarize the mechanics of using LINEST in Excel. Since it is an array function, select 6 cells (2 columns, 3 rows). You can select up to 5 rows (10 cells) and get even more statistics, but we usually only need the first six. Hit the equal sign key to tell Excel you are about to enter a function. Type LINEST(, use the mouse to select your y-data, type a comma, use the mouse to select your x-data, type another comma, then type true twice separated by a comma and close the parentheses. DON'T HIT ENTER. Instead, hold down shift and control and then press enter. This is the way to execute an array function. The second image below shows the results of the function. From left to right, the first row displays the slope and y-intercept, the second row displays the standard error of the slope and y-intercept. The first element in the third row displays the correlation coefficient. I actually don't know what the second element is. Look it up if you are int
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 http://www.chem.utoronto.ca/coursenotes/analsci/stats/ErrRegr.html in the slope and intercept of the calculated regression line. This can http://cameron.econ.ucdavis.edu/excel/ex53bivariateregressionstatisticalinference.html 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 how to 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 how to calculate 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 calibration function) can be expressed in terms of the regression residuals, (yi − ): The greater these resdiuals, the greater the uncertainty in where the true regression line actually lies. The uncertainty in the regression is therefore calculated in terms of these residuals. Technically, this is the standard error of the regression, sy/x: Note that there are (n − 2) degrees of freedom in calcu
table (often this is skipped). Interpreting the regression coefficients table. Confidence interval for the slope parameter. Testing hypothesis of zero slope parameter. Testing hypothesis of slope parameter equal to a particular value other than zero. Testing overall significance of the regressors. Predicting y given values of regressors. Fitted values and residuals from regression line. Other regression output. This handout is the place to go to for statistical inference for two-variable regression output. REGRESSION USING THE DATA ANALYSIS ADD-IN This requires the Data Analysis Add-in: see Excel 2007: Access and Activating the Data Analysis Add-in The data used are in carsdata.xls The method is explained in Excel 2007: Two-Variable Regression using Data Analysis Add-in Regression of CARS on HH SIZE led to the following Excel output: The regression output has three components: Regression statistics table ANOVA table Regression coefficients table. INTERPRET REGRESSION STATISTICS TABLE Explanation Multiple R 0.894427 R = square root of R2 R Square 0.8 R2 = coefficient of determination Adjusted R Square 0.733333 Adjusted R2 used if more than one x variable Standard Error 0.365148 This is the sample estimate of the standard deviation of the error u Observations 5 Number of observations used in the regression (n) The Regression Statistics Table gives the overall goodness-of-fit measures: R2 = 0.8 Correlation between y and x is 0.8944 (when squared gives correlation squared = 0.8 = R2 ). Adjusted R2 is discussed later under multiple regression. The standard error here refers to the estimated standard deviation of the error term u. It is sometimes called the standard error of the regression. It equals sqrt(SSE/(n-k)). It is not to be confused with the standard error of y itself (from descriptive statistics) or with the standard errors of the regression coefficients given below. INTERPRET ANOVA TABLE df SS MS F Signifiance F Regression 1 1.6 1.6 12 0.04519 Residual 3 0.4 0.133333 Total 4 2.0 The ANOVA (analysis of variance) table splits the sum of squares into its components. Total sums of squares = Residual (or error) sum of squares + Regression (or explained) sum of squares. Thus Σ i (yi - ybar)2 = Σ i (yi - yhati)2 + Σ i (yhati - ybar)2 where yhati is the value of yi predicted from the regression line and ybar is the sample mean of y. For example: R2 = 1 - Residual SS / Total SS (general formula for R2) = 1 - 0.4/2.0 (fro