sas code calculate from linear regression equation

SAS CODE CALCULATE FROM LINEAR REGRESSION EQUATION HOW TO

While holding the other variables at a constant value. The regression coefficients predict the change in the response for one unit change in an explanatory variable Interpretation of the regression coefficientsįor the original (unstandardized) data, the intercept estimate predicts the value of the response when the explanatory variables are all zero. (A similar proof handles multiple explanatory variables.) Thus the STB option on the MODEL statement does not need to standardize any data! It produces the standardized estimates by setting the intercept term to 0 and dividing the parameter estimates by the ratio of standard deviations, as noted in the documentation. Furthermore, the coefficient B1 = b1*(s X/s Y) is the original parameter estimate 'divided by the ratio of the sample standard deviation of the dependent variable to the sample standard deviation of the regressor,' just as the PROC REG documentation states and just as we saw in the PROC REG output in the previous section. The intercept estimate is b0 = c Y - b1*c Y, which implies that B0 = 0. Regression estimates for a simple linear regression model. That is,Ĭ Y and c X are the sample means and s Y and s X are the sample standard deviations.

U and V are standardized versions of Y and X, respectively.

The analysis in the previous section holds for any linear transformation of linearly related random variables. The effect of standardizing variables on regression estimates For example, if X is measured in inches and Y is measured in pounds, then the quantities remain linearly related if you measure X in centimeters and measure Y in 'kilograms from 20 kg.' The physical significance of this result is that linear relationships persist no matter what units you choose to measure the variables. If you define B0 = (b0 + b1*c X - c Y) / s YĪnd B1 = b1*(s X/s Y), then U = B0 + B1*V, which shows that the transformed variables (U and V) are linearly related. If you solve for X and Y and plug the expressions into the equation for the linear relationship, you find that the new random variables are related by What happens to this linear relationship if you apply linear transformations to X and Y? Suppose X is a random variable and Y = b0 + b1*X for some constants b0 and b1. Mathematically, you can use a algebra to understand how linear transformations affect the relationship between two linearly dependent random variables. Linear transformations of random variables Notice, however, that scale-dependent statistics such as standard errors and covariance of the betas will not be the same for the two analyses.

Furthermore, the t values and p-values for the slope parameters are equivalent because these statistics are scale- and translation-invariant. The parameter estimates for the standardized data are equal to the STB estimates for the original data. METHOD=STD standardizes variables according to StdX = (X - mean(X)) / std(X) */ proc stdize data=Sashelp.Class out=ClassStd method= std OPREFIX SPREFIX= Std Standardized variables have the names 'StdX' where X was the name of the original variable. * Put original and standardized variables into the output data set.

The following call to PROC REG uses the STB option to compute the standardized parameter estimates for a model that predicts the weights of 19 students from heights and ages:

SAS CODE CALCULATE FROM LINEAR REGRESSION EQUATION HOW TO

The following example uses continuous response and explanatory variables, but there is a SAS Usage Note that describes how to standardize classification variables. This section uses PROC STDIZE and PROC REG to 'prove by example' that the standardized regression estimates for data are equal to the estimates that you obtain by standardizing the data. One of my college physics professors used to smile and say 'I will now prove this by example' when he wanted to demonstrate a fact without proving it mathematically. It also derives how regression coefficients change after a linear transformation of the variables. This article uses SAS to demonstrate how parameter estimates for the original variables are related to parameter estimates for standardized variables. The SAS documentation for the STB option states, 'a standardized regression coefficient is computed by dividing a parameter estimate by the ratio of the sample standard deviation of the dependent variable to the sample standard deviation of the regressor.' Although correct, this definition does not provide an intuitive feeling for how to interpret the standardized regression estimates. A SAS programmer recently asked how to interpret the 'standardized regression coefficients' as computed by the STB option on the MODEL statement in PROC REG and other SAS regression procedures.

Sas code calculate from linear regression equation