# Sufficient linearity between predictor and response variables?

#### lc1810

##### New Member
Hello everyone,

for a multiple regression I am currently trying to understand if there is sufficient linearity between my predictor and response variables to see whether I can carry on with a regular linear regression.
I have three models, with one dependent and the same three independent/control variables each.
The dataset contains expert survey data on >200 political parties, with variables such as "use of pluralist/populist rhethoric" or "position of party on political spectrum - left/right". All variables used are scaled 0-10 and the values represent the average of all participating experts' answers. n=207

I tried testing for linearity with a scatterplot but am not quite sure whether the results are clear enough to indicate linearity.
I attached the scatterplots(matrix) (correlation- + LOESS-graph).

Do you think there is sufficient linearity?

I also tried testing for linearity using dummy variables for the three independent variables in the regression, each of which representing 1/5 of the 0-10 scale.
My supervisor suggested this to me, however I am not sure how to interpret the results. Is it enough for the regression-coefficient to consistantly rise/fall with each further dummy category? (I also attached an example of said regression with dummys)

I would be so thankful for help as I lost so much time looking for an answer!

Best regards
Leo

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#### noetsi

##### Fortran must die
I would also run box tidwel which is a test of linearity. If your predictor variables are dummies than you don't have to worry about linearity. They are always linear.

#### lc1810

##### New Member
@noetsi thank you so much for the tip!
Regarding the dummy variables: I recoded the predictor variables from their scale of 0-10 into five dummy variables (e.g. dummy1 = 0-2 / dummy2 = 2-4 / dummy3 = 4-6 / dummy4 = 6-8 / dummy5 = 8-10) and then took the dummy variables into the regression model instead of the metric scaled predictor variables. That is what the regression output is. According to my supervisor it should then be possible to interpret the results and see whether there is linearity between predictor and response variables.

#### noetsi

##### Fortran must die
If you have a dummy predictor then there will always be a linear relationship between the predictor and response variable. You could run box tidwel, but by definition the relationship will be linear.

I have never seen a scale divided into dummies that way. Does it make substantive sense to say someone, for example on a scale of 1-1 lies in a specific dummy.