Use a colon between two characters as a regressor in lm ()

Question

What does this mean when we put a colon : between two characters? I am sure this does not speak from character A to character B.

Here is the code:

 fit9=lm(Sales~.+Income:Advertising+Price:Age,data=Carseats) Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 6.5755654 1.0087470 6.519 2.22e-10 *** CompPrice 0.0929371 0.0041183 22.567 < 2e-16 *** Income 0.0108940 0.0026044 4.183 3.57e-05 *** Advertising 0.0702462 0.0226091 3.107 0.002030 ** Population 0.0001592 0.0003679 0.433 0.665330 Price -0.1008064 0.0074399 -13.549 < 2e-16 *** ShelveLocGood 4.8486762 0.1528378 31.724 < 2e-16 *** ShelveLocMedium 1.9532620 0.1257682 15.531 < 2e-16 *** Age -0.0579466 0.0159506 -3.633 0.000318 *** Education -0.0208525 0.0196131 -1.063 0.288361 UrbanYes 0.1401597 0.1124019 1.247 0.213171 USYes -0.1575571 0.1489234 -1.058 0.290729 Income:Advertising 0.0007510 0.0002784 2.698 0.007290 ** Price:Age 0.0001068 0.0001333 0.801 0.423812 

I could not understand why the two additional regressions Income:Advertising and Price:Age mean?

Answer 1

As noted in the comments above,: denotes the term interaction between regressors. If you want to consider each regressor independently and the interaction, you can use x1*x2 , which is the same as x1 + x2 + x1:x2 .