Formula For Multiple Standard Error Of Estimate
Contents |
is used to predict a single dependent variable (Y). The predicted value of Y is a linear transformation of the X variables such that the sum of squared deviations of the observed and predicted Y is a minimum. The computations are more complex, however, because the interrelationships among all the variables must be taken into account in the weights assigned to the variables. The interpretation of the results of a multiple regression multiple regression example problems analysis is also more complex for the same reason. With two independent variables the prediction of Y is expressed by
Standard Error Multiple Regression
the following equation: Y'i = b0 + b1X1i + b2X2i Note that this transformation is similar to the linear transformation of two variables discussed in the previous chapter except that the multiple regression equation example w's have been replaced with b's and the X'i has been replaced with a Y'i. The "b" values are called regression weights and are computed in a way that minimizes the sum of squared deviations in the same manner as in simple linear regression. The difference is that in simple
Multiple Regression Equation With 3 Variables
linear regression only two weights, the intercept (b0) and slope (b1), were estimated, while in this case, three weights (b0, b1, and b2) are estimated. EXAMPLE DATA The data used to illustrate the inner workings of multiple regression will be generated from the "Example Student." The data are presented below: Homework Assignment 21 Example Student PSY645 Dr. Stockburger Due Date
Y1 Y2 X1 X2 X3 X4 125 113 13 18 25 11 158 115 39 18 59 30 207 126 52 how to calculate multiple regression by hand 50 62 53 182 119 29 43 50 29 196 107 50 37 65 56 175 135 64 19 79 49 145 111 11 27 17 14 144 130 22 23 31 17 160 122 30 18 34 22 175 114 51 11 58 40 151 121 27 15 29 31 161 105 41 22 53 39 200 131 51 52 75 36 173 123 37 36 44 27 175 121 23 48 27 20 162 120 43 15 65 36 155 109 38 19 62 37 230 130 62 56 75 50 162 134 28 30 36 20 153 124 30 25 41 33 The example data can be obtained as a text file and as an SPSS/WIN file from this web page. If a student desires a more concrete description of this data file, meaning could be given the variables as follows: Y1 - A measure of success in graduate school. X1 - A measure of intellectual ability. X2 - A measure of "work ethic." X3 - A second measure of intellectual ability. X4 - A measure of spatial ability. Y2 - Score on a major review paper. UNIVARIATE ANALYSIS The first step in the analysis of muthe ANOVA table (often this is skipped). Interpreting the regression coefficients table. Confidence intervals for the slope parameters. Testing for statistical significance of coefficients Testing hypothesis on a slope parameter. Testing overall significance of the regressors. Predicting y given
Multiple Correlation Coefficient Formula
values of regressors. Excel limitations. There is little extra to know beyond regression with one
Multiple Correlation Coefficient In R
explanatory variable. The main addition is the F-test for overall fit. MULTIPLE REGRESSION USING THE DATA ANALYSIS ADD-IN This requires the Data standard error multiple linear regression Analysis Add-in: see Excel 2007: Access and Activating the Data Analysis Add-in The data used are in carsdata.xls We then create a new variable in cells C2:C6, cubed household size as a regressor. Then in cell C1 http://www.psychstat.missouristate.edu/multibook/mlt06m.html give the the heading CUBED HH SIZE. (It turns out that for the se data squared HH SIZE has a coefficient of exactly 0.0 the cube is used). The spreadsheet cells A1:C6 should look like: We have regression with an intercept and the regressors HH SIZE and CUBED HH SIZE The population regression model is: y = β1 + β2 x2 + β3 x3 + u It is assumed that the error http://cameron.econ.ucdavis.edu/excel/ex61multipleregression.html u is independent with constant variance (homoskedastic) - see EXCEL LIMITATIONS at the bottom. We wish to estimate the regression line: y = b1 + b2 x2 + b3 x3 We do this using the Data analysis Add-in and Regression. The only change over one-variable regression is to include more than one column in the Input X Range. Note, however, that the regressors need to be in contiguous columns (here columns B and C). If this is not the case in the original data, then columns need to be copied to get the regressors in contiguous columns. Hitting OK we obtain The regression output has three components: Regression statistics table ANOVA table Regression coefficients table. INTERPRET REGRESSION STATISTICS TABLE This is the following output. Of greatest interest is R Square. Explanation Multiple R 0.895828 R = square root of R2 R Square 0.802508 R2 Adjusted R Square 0.605016 Adjusted R2 used if more than one x variable Standard Error 0.444401 This is the sample estimate of the standard deviation of the error u Observations 5 Number of observations used in the regression (n) The above gives the overall goodness-of-fit measures: R2 = 0.8025 Correlation between y and y-hat is 0.8958 (when squared gives 0.8025). Adjusted R2 = R2 - (1-R2 )*(k-1)/(n-k) = .8025 - .1975*2
Need some help calculating standard error of multiple regression coefficients Tweet Welcome to Talk Stats! Join the discussion today by registering your FREE account. Membership benefits: • http://www.talkstats.com/showthread.php/5056-Need-some-help-calculating-standard-error-of-multiple-regression-coefficients Get your questions answered by community gurus and expert researchers. • Exchange your learning and research experience among peers and get advice and insight. Join Today! + Reply to Thread Page 1 of 2 1 2 Last Jump to page: Results 1 to 15 of 16 Thread: Need some help calculating standard error of multiple regression coefficients Thread Tools Show Printable Version multiple regression Email this Page… Subscribe to this Thread… Display Linear Mode Switch to Hybrid Mode Switch to Threaded Mode 07-21-200806:52 PM #1 joseph.ej View Profile View Forum Posts Give Away Points Posts 2 Thanks 0 Thanked 0 Times in 0 Posts Need some help calculating standard error of multiple regression coefficients Hello. I am an undergrad student not very familiar with advanced statistics. standard error multiple Thus, I figured someone on this forum could help me in this regard: The following is a webpage that calculates estimated regression coefficients for multiple linear regressions http://people.hofstra.edu/stefan_Waner/realworld/multlinreg.html. I would like to add on to the source code, so that I can figure out the standard error for each of the coefficients estimates in the regression. I don't understand the terminology in the source code, so I figured someone here might in order to show me how to calculate the std errors. I would like to be able to figure this out as soon as possible. Thank you for your help. Reply With Quote 07-21-200807:50 PM #2 Dragan View Profile View Forum Posts Super Moderator Location Illinois, US Posts 1,958 Thanks 0 Thanked 196 Times in 172 Posts Originally Posted by joseph.ej Hello. I am an undergrad student not very familiar with advanced statistics. Thus, I figured someone on this forum could help me in this regard: The following is a webpage that calculates estimated regression coefficients for multiple linear regressions http://people.hofstra.edu/stefan_Waner/realworld/multlinreg.html. I would like to add on to the source code, so t
be down. Please try the request again. Your cache administrator is webmaster. Generated Fri, 14 Oct 2016 11:56:05 GMT by s_ac4 (squid/3.5.20)