# Should there be an "i" in a regression equation?

I have developed a general linear model to predict my dependent variable Y. I am unsure on how to present my equation.

Should it be: (not sure if the i should be there or not)

$Yi= .432 + .320 Age_i + .520 WE_i + .300 JP1_i + .210 JP2_i$

or

$Y= .432 + .320 Age + .520 WE + .300 JP1 + .210 JP2$

Where:

WE= work experience; JP= Job Position; JP1= floor level staff; JP2= Managers;

• You should add the error terms too. Commented Apr 27, 2014 at 15:03

The $i$'s usually index the observations in the sample used to fit the model, so if you simply want to present the predictive equation for a single new observation, there's no need for them. Also be careful not to confuse the random variable, its observed values, & the fitted values: if you've previously defined $Y_i$ as the $i$th observed value of the dependent variable then

$$Y_i= .432 + .320 Age_i + .520 WE_i + .300 JP1_i + .210 JP2_i$$

is wrong because it omits the residual term. A common notational scheme is $Y$ for the random variable, $y$ for its observed values, & $\hat{y}$ for the fits.

I'd suggest you write the equation like this

$$\hat y = 0.432 + 0.320 x_1 + 0.520 x_2 + 0.300 x_3 + 0.210 x_4$$

(defining the terms appropriately) or like this

$$\mathrm{Salary} = 0.432 + (0.320 \times \mathrm{Age}) + (0.520 \times \mathrm{WE}) + (0.300 \times \mathrm{JP1}) + (0.210 \times \mathrm{JP2})$$

rather than mixing up formal mathematical notation with a word equation. NB:

1. Italics emphasize single-letter place-holders for numbers, functions, or operators that you define. Don't use them in word equations. (In any case, in the LaTeX math environment fluff gives the product $fluff$; \mathit{fluff} gives the italicized word $\mathit{fluff}$.)

2. S.I. (& I'd wager any other convention written down as such) mandates showing leading zeroes before decimal points.

3. The brackets in the word equation aren't necessary, but your readers may not know that.

4. With many terms a table of coefficients is more convenient.

Both are correct, but if you use the i 's they should preferably be subscripts:

$Y_i = .432 + .320Age_i + .520WE_i + .300JP1_i + .210JP2_i$

If you don't use the i's then the equation is about vectors.