I have one continuous dependent variable and three categorical independent variables(having 2, 2 and 3 categories). My questions are:
1. would multiple linear regression is good to explain relationship?
2. if yes, how can I test linearity of categorical variables? or I should not be bothered about linearity in the case of categorical data.
3. if multiple regression is not good to test than any alternative test?
4. please provide any guide/tutorial/paper/video about multiple regression having only categorical data.
Regards,
Darshan
First, code each factor with the appropriate number of dummy variables.
Dummy for each level above the base level.
d1 = 1 if in cat 1 level 1; 0 otherwise
d2 = 1 if in cat 2 level 1; 0 otherwise
d3 = 1 if in cat 3 level 1; 0 otherwise
d4 = 1 if in cat 3 level 2; 0 otherwise
Then regress y ~d1+d2+d3+d4+d1d2+d1d3+d1d4+d2d3+d2d4+d1d2d3+d1d2d4
These will yield various comparisons and contrast between factors and test the level of significance.
This ANCOVA tests comparison and contrasts between group means. Dummy variables are dichotomous and can not be considered linear in this form.
EXAMPLE, y = height and d = gender (1 if male and 0 if female) then the model
y=b0+b1d shows the mean mu0 for females (d=0) is b0 and the mean mu1 for males the mean is b0+b1; hence using a t-test to determine if b1=0 is equivalent to testing if mu1 - mu0 = 0; that is, is there a significant difference in means.
Hope this helps.
1-Yes.
2-The latter.
3-You might be suggested to use ANOVA instead, but the difference is very little if not nonexistent.
4-Just do regression with care. Properly code your categorical predictors and interpret. You can search for videos on two/three-way ANOVA because you might not find a video about multiple regression with categorical predictors.
Rebecca, I cannot see how ANCOVA is related here.
As already mentioned by Dr. Iysoy, an ANOVA approach would be easier for finding detailed tutorials, as well as for interpretation of the results.
