linear regression equation calculator with 1980

Suppose we want to predict job performance of Chevy mechanics based on mechanical aptitude test scores and test scores from personality test that measures conscientiousness. This equation is a straight-forward generalization of the case for one independent variable. The equation for a with two independent variables is:

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. Note that terms corresponding to the variance of both X variables occur in the slopes. For example, X 2 appears in the equation for b 1. In the two variable case, the other X variable also appears in the equation.

It's simpler for k=2 IVs, which we will discuss here.įor the one variable case, the calculation of b and a was:Īt this point, you should notice that all the terms from the one variable case appear in the two variable case. The prediction equation is:įinding the values of b is tricky for k>2 independent variables, and will be developed after some matrix algebra. Again we want to choose the estimates of a and b so as to minimize the sum of squared errors of prediction. We still have one error and one intercept. Note that we have k independent variables and a slope for each. We can extend this to any number of independent variables: 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. With one independent variable, we may write the regression equation as: How is it possible to have a significant R-square and non-significant b weights? What are the three factors that influence the standard error of the b weight? Write a regression equation with beta weights in it. Why do we report beta weights (standardized b weights)? What happens to b weights if we add new variables to the regression equation that are highly correlated with ones already in the equation? multiple regression?ĭescribe R-square in two different ways, that is, using two distinct formulas. What is the difference in interpretation of b weights in simple regression vs. Write a raw score regression equation with 2 ivs in it. These programs incorporate the most important features of programs previously developed in this laboratory for an IBM 370 or a DECsystem-10 computer, and demonstrate the availability of adequate statistical analyses to laboratories without access to large centralized computer facilities.Regression with Two Independent Variables 3) A third program is used for routine Within-Lab Quality Control: it calculates within-assay and between-assay precision, utilizing an analysis of variance (ANOVA) with a components of variance estimation. As such, it is more flexible and versatile than the logit-log method. This is the equivalent to the use of the logit-log method, with provision for adjustment for the position of the 0% and 100% response. 2) The second program uses the 'four parameter logistic model' to describe the dose responses curve and perform dose interpolation. This program also provides: dose interpolation for unknowns an estimate of the precision (percent coefficient of variation) for each result corrections for variable sample volumes or recoveries and the mean and standard error of the mean for samples analyzed in replicate. We have developed three programs for data processing for radioimmunoassays RIA implemented on a small, inexpensive, programmable calculator (Texas Instrument Co., Model 59): 1) The first program performs a weighted logit-log regression for analysis of the RIA standard curve, and provides several descriptive statistics: slope, intercept, ED50 (and their corresponding standard errors), residual variance, and correlation coefficient.

Linear regression equation calculator with 1980