Multiple Regression Equation Standard Error Calculator
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Free Statistics Calculators: Home > Regression Calculators Regression Calculators Below you will find descriptions and links to 14 free statistics calculators for computing values associated with regression studies.
Multiple Regression Calculator
If you like, you may also use the search page to calculate standard error multiple regression help you find what you need. A-priori Sample Size Calculator for Multiple Regression This calculator will tell you
Standard Error Multiple Regression Coefficients
the minimum required sample size for a multiple regression study, given the desired probability level, the number of predictors in the model, the anticipated effect size, and the desired how to calculate standard error of regression coefficient statistical power level. Adjusted R-square Calculator (Population R-square) This calculator will compute an adjusted R2 value (i.e., the population squared multiple correlation), given an observed (sample) R2, the number of predictors in the model, and the total sample size. Beta (Type II Error Rate) Calculator for Multiple Regression This calculator will tell you the beta level for your study multiple regression analysis (i.e., the Type II error rate), given the observed probability level, the number of predictors, the observed R2, and the sample size. Confidence Interval Calculator for a Predicted Value of a Regression Equation This calculator will compute the 99%, 95%, and 90% confidence intervals for a predicted value of a regression equation, given a predicted value of the dependent variable, the standard error of the estimate, the number of predictors in the model, and the total sample size. Critical F-value Calculator This calculator will tell you the critical value of the F-distribution, given the probability level, the numerator degrees of freedom, and the denominator degrees of freedom. Effect Size Calculator for Multiple Regression This calculator will tell you the effect size for a multiple regression study (i.e., Cohen's f2), given a value of R2. f-square Effect Size Confidence Interval Calculator This calculator will compute the 99%, 95%, and 90% confidence intervals for the f2 effect size associated with a multiple regression study, given the f2 value, the number of predictors in the model, and the
the ANOVA table (often this is skipped). Interpreting the regression coefficients table. Confidence intervals for the slope parameters. Testing for statistical significance of coefficients Testing
Adjusted R Squared
hypothesis on a slope parameter. Testing overall significance of the regressors. Predicting coefficient of determination y given values of regressors. Excel limitations. There is little extra to know beyond regression with one
Linear Regression
explanatory variable. The main addition is the F-test for overall fit. MULTIPLE REGRESSION USING THE DATA ANALYSIS ADD-IN This requires the Data Analysis Add-in: see Excel 2007: Access and Activating http://www.danielsoper.com/statcalc/category.aspx?id=15 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 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 http://cameron.econ.ucdavis.edu/excel/ex61multipleregression.html 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 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. E
window How to enter data How to enter dates Missing values Data checking How to save data Statistics Variables Filters Graphs Add graphical objects Reference lines F7 - Repeat key https://www.medcalc.org/manual/regression.php Notes editor File menu New Open Save Save as Add file Export Page setup Print Properties Exit Edit menu Undo Cut Copy Paste Delete Select all Find Find & http://faculty.cas.usf.edu/mbrannick/regression/Reg2IV.html replace Go to cell Fill Insert - Remove Transpose View menu Spreadsheet Show formulas Show gridlines Contents bar Toolbars Status bar Full screen Format menu Font Increase font size Decrease multiple regression font size Spreadsheet Format graph Graph legend Reset graph titles and options Tools menu Sort rows Exclude & Include Fill column Stack columns Generate random sample Create groups Create groups form quantiles Create random groups Create user-defined groups Rank cases Percentile ranks z-scores Power transformation Edit variables list Edit filters list Select variable for case identification Enter key moves calculate standard error cell pointer Options Statistics menu Summary statistics Outlier detection Distribution plots Histogram Cumulative frequency distribution Normal plot Dot plot Box-and-whisker plot Correlation Correlation coefficient Partial correlation Rank correlation Scatter diagram Regression Regression Scatter diagram & regression line Multiple regression Logistic regression Probit regression (Dose-Response analysis) Nonlinear regression T-tests One sample t-test Independent samples t-test Paired samples t-test Rank sum tests Signed rank sum test (one sample) Mann-Whitney test (independent samples) Wilcoxon test (paired samples) Variance ratio test (F-test) ANOVA One-way analysis of variance Two-way analysis of variance Analysis of covariance Repeated measures analysis of variance Kruskal-Wallis test Friedman test Crosstabs Chi-squared test Fisher's exact test McNemar test Cochran's Q test Relative risk & Odds ratio Frequencies bar charts Survival analysis Kaplan-Meier survival analysis Cox proportional-hazards regression Meta-analysis Introduction Continuous measure Correlation Proportion Relative risk Risk difference Odds ratio Area under ROC curve Generic inverse variance method Serial measurements Reference intervals Reference interval Age-related reference interval Method comparison & evaluation Bland & Altman plot Bland-Altman plot with multiple measurements per subject Comparison of multiple methods Mounta
ways, that is, using two distinct formulas. Explain the formulas. What happens to b weights if we add new variables to the regression equation that are highly correlated with ones already in the equation? Why do we report beta weights (standardized b weights)? Write a regression equation with beta weights in it. What are the three factors that influence the standard error of the b weight? How is it possible to have a significant R-square and non-significant b weights? Materials The Regression Line With one independent variable, we may write the regression equation as: Where Y is an observed score on the dependent variable, a is the intercept, b is the slope, X is the observed score on the independent variable, and e is an error or residual. We can extend this to any number of independent variables: (3.1) Note that we have k independent variables and a slope for each. We still have one error and one intercept. Again we want to choose the estimates of a and b so as to minimize the sum of squared errors of prediction. The prediction equation is: (3.2) Finding the values of b is tricky for k>2 independent variables, and will be developed after some matrix algebra. It's simpler for k=2 IVs, which we will discuss here. For the one variable case, the calculation of b and a was: For the two variable case: and At this point, you should notice that all the terms from the one variable case appear in the two variable case. In the two variable case, the other X variable also appears in the equation. For example, X2 appears in the equation for b1. Note that terms corresponding to the variance of both X variables occur in the slopes. Also note that a term corresponding to the covariance of X1 and X2 (sum of deviation cross-products) also appears in the formula for the slope. The equation for a with two independent variables is: This equation is a straight-forward generalization of the case for one independent variable. A Numerical Example Suppose we want to predict job performance of Chevy mechanics based on mechanical aptitude test scores and test scores f