How To Calculate Standard Error Of Intercept In Excel
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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 error in slope excel standard error of the slope and y-intercept are not give. To find these statistics, use the
How To Calculate Error In Slope
LINEST function instead. The LINEST function performs linear regression calculations and is an array function, which means that it returns more than one standard deviation of slope formula value. Let's do an example to see how 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
How To Calculate Standard Error Of Slope And Intercept
spring stretched (s). Hooke's law states the F=-ks (let's ignore 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 linest excel mac it should be plotted on the x-axis. Therefore, s is the dependent variable and should be 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 er
STEYX and FORECAST. Fitting a regression line using Excel function LINEST. Prediction using Excel function TREND. For most purposes these Excel functions are unnecessary. It is easier to instead use the Data Analysis Add-in for Regression. REGRESSION USING EXCEL FUNCTIONS INTERCEPT,
Formula For Calculating Error In Slope
SLOPE, RSQ, STEYX and FORECAST The data used are in carsdata.xls The population regression model is:
How To Find Standard Deviation Of Slope And Intercept
y = β1 + β2 x + u We wish to estimate the regression line: y = b1 + b2 x The individual formula for finding error in slope functions INTERCEPT, SLOPE, RSQ, STEYX and FORECAST can be used to get key results for two-variable regression INTERCEPT(A1:A6,B1:B6) yields the OLS intercept estimate of 0.8 SLOPE(A1:A6,B1:B6) yields the OLS slope estimate of 0.4 RSQ(A1:A6,B1:B6) yields the R-squared of 0.8 http://www.fiz-ix.com/2013/01/finding-standard-error-of-slope-and-y-intercept-using-linest-in-excel-linear-regression-in-physics-lab/ STEYX(A1:A6,B1:B6) yields the standard error of the regression of 0.36515 0.8 FORECAST(6,A1:A6,B1:B6) yields the OLS forecast value of Yhat=3.2 for X=6 (forecast 3.2 cars for household of size 6). Thus the estimated model is y = 0.8 + 0.4*x with R-squared of 0.8 and estimated standard deviation of u of 0.36515 and we forecast that for x = 6 we have y = 0.8 + 0.4*6 = 3.2. REGRESSION USING EXCEL FUNCTION LINEST The individual http://cameron.econ.ucdavis.edu/excel/ex54regressionwithlinest.html function LINEST can be used to get regression output similar to that several forecasts from a two-variable regression. This is tricky to use. The formula leads to output in an array (with five rows and two columns (as here there are two regressors), so we need to use an array formula. We consider an example where output is placed in the array D2:E6. First in cell D2 enter the function LINEST(A2:A6,B2:B6,1,1). Then Highlight the desired array D2:E6 Hit the F2 key (Then edit appears at the bottom left of the dpreadsheet). Finally Hit CTRL-SHIFT-ENTER. This yields where the results in A2:E6 represent Slope coeff Intercept coeff St.error of slope St.error of intercept R-squared St.error of regression F-test overall Degrees of freedom (n-k) Regression SS Residual SS In particular, the fitted regression is CARS = 0.4 + 0.8 HH SIZE with R2 = 0.8 The estimated coefficients have standard errors of, respectively, 0.11547 and 0.382971. To get just the coefficients give the LINEST command with the last entry 0 rather than 1, ie. LINEST(A2:A6,B2:B6,1,0), and then highlight cells A8:B8, say, hit F2 key, and hit CTRL-SHIFT-ENTER. LINEST can be extended to multiple regression (more than an intercept and one regressor). Then the first two rows of output are extended to number of columns equals number of regressors (including constant) and the last three rows are the same as earlier.
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