There is some flexibility in the way linear dependencies among variables can be specified. The following lines are equivalent ways of specifying that the variable yyy depends linearly on the variables xxx1, xxx2 and error1.
yyy = xxx1 xxx2 error1
yyy <- xxx1 xxx2 error1
yyy = xxx1 + xxx2 + error1
yyy = ()xxx1 + ()xxx2 + ()error1
yyy = ()*xxx1 + ()*xxx2 + ()*error1
yyy = () * xxx1 + () * xxx2 + () * error1
As those examples illustrate,
•Plus signs (+) and asterisks (*) are optional. Use them if you think it makes the syntax more readable.
•Empty parentheses represent regression weights that need to be estimated. The empty parentheses are optional.
•"=" and "<-" are equivalent in meaning.
•White space (spaces and tab characters) can be used anywhere to make the text easier to read, except that a line that begins with white space is treated as a continuation of the preceding line.
If means and intercepts are explicit model parameters (see Estimate means and intercepts,) an intercept must appear in each regression equation, as follows.
yyy = () + xxx1 xxx2 error1
yyy = () + xxx1 + xxx2 + error1
yyy = () + ()xxx1 + ()xxx2 + ()error1
yyy = () + ()*xxx1 + ()*xxx2 + ()*error1
The empty parentheses and the plus sign in "() +" are required in order to specify the presence of an intercept. This is the only context in which empty parentheses and the plus sign are not optional.
Each of the following equivalent lines specifies that error1 has a fixed weight of 1 in predicting yyy while the weights for xxx1 and xxx2 are unconstrained.
yyy = xxx1 xxx2 (1) error1
yyy = xxx1 + xxx2 + (1) error1
yyy = () xxx1 + () xxx2 + (1) error1
Each of the following equivalent lines specifies that the weight for xxx1 is named alpha and the weight for xxx2 is also named alpha. This means that the two regression weight estimates are constrained to be equal. The weight for error1 is also fixed at a constant value of 1.
yyy = (alpha )xxx1 (alpha) xxx2 (1) error1
yyy = (alpha) xxx1 + (alpha) xxx2 + (1) error1
In the following line, the intercept in the equation for predicting yyy is named gamma, and the weight for error1 is fixed at a constant 1.
yyy = (gamma) + ()xxx1 + ()xxx2 + (1)error1