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What does it mean when we put a colon : between two characters? I'm sure it's not saying 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 couldn't understand why does two extra regressors Income:Advertising and Price:Age mean?
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To express the idea of an interaction in the R modeling language, we need to introduce two new operators. The colon (:) is used to indicate an interaction between two or more variables in model formula.
Summary: R linear regression uses the lm() function to create a regression model given some formula, in the form of Y~X+X2. To look at the model, you use the summary() function. To analyze the residuals, you pull out the $resid variable from your new model.
The lm() function Note that the formula argument follows a specific format. For simple linear regression, this is “YVAR ~ XVAR” where YVAR is the dependent, or predicted, variable and XVAR is the independent, or predictor, variable.
As noted in the comments above, : denotes an interaction term between regressors. If you want to consider each regressor on its own and the interaction, then you can use x1*x2 which is the same as x1 + x2 + x1:x2.
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