# Help interpreting a multiple regression

In R I get a multiple regression output like the following: I need to know what the column headings translate into. Such as which column would give me b in an equation, which would give me a, what would be x and y values. More importantly, I need to know if I have all the numbers I need to interpret the equation y = a + bx (and preferably what numbers go where).

This is for an assignment, and while I'm not looking for an exact answer, I need enough info to answer the following: "Discuss the message of your regression results (what the final equation suggests about the social world). Rely primarily on the bs here, noting how they impact each predictor, and why each may seem to have the kind of impact it seems to."

• Note that you don't have a model $y = a + bx$ here; it's more like $y = b_0 + b_1 x_1 + b_2 x_2 + b_3 x_3 + \dots$. Why is the row for sex blank in what you show us? – Nick Cox Mar 23 '17 at 16:36

In the R output you have posted:

Estimate = Your estimate of the effect $\beta$ (each $b$ in your $y=a+bx$) with respect to $y$ for each independent variable in your model.

Std.Error = The standard error for each $\beta$ estimate

t value = The t-statistic for assessing the significance of the variable at a given level

$Pr>|t|$ = The p.value for assessing significance of the respective variable in your model.

Note that the intercept estimate will correspond to the $a$ in your $y=a+bx$.

Note that this just explains each column, and doesn't go into the overall interpretation of the model (I assume this is what you are after wanting a rough answer). For what each element means with respect to interpretation, I would recommend reading Chapter 3 and Chapter 4 of Wooldridge (2006), which was helpful for me when I first started.

I hope that helps, it is by no means comprehensive but hopefully sheds a little light for understanding the R output.

Bibliography:

Wooldridge, J. M. 2006. Introductory econometrics: a modern approach. Mason, OH, Thomson/South-Western.