You could use linear regression, however you would need ot convert your categorical predictor into a dummy variable (dichotomous). I wonder how many answer categories does the predictor have? Is Likert type?
In this situation, I would have used ANOVA. In ANOVA, independent variables are of nominal scale (categorical example : 3 set of pricing , so level 1,2 , 3) ) and dependent variable is continuous (example: sales) or at least interval scaled.
I have done some experiment, where I have set independent variables are of nominal scale and dependent scales are of continuous (example : sales) or scale ( example: purchase intention in the of 1-5 likert scale)
I think it depends on number of dependent, independent, and control variables.
Case 1: There is only one continuous dependent variable, there are one plus categorical independent variables, and there is no control variable at all, then you can go for ANOVA.
Case2: There is only one continuous dependent variable, there are one plus categorical independent variables, and there are one plus control variables, then you can go for ANCOVA.
Case3: There are two or more continuous dependent variables, there are one plus categorical independent variables, and there is no control variable at all, then you can go for MANOVA.
Case 4: There are two or more continuous dependent variables, there are one plus categorical independent variables, and there are one plus control variables, then you can go for MANCOVA.
Case5: If there is only one continuous dependent variable, there is only one categorical independent variable (i.e. dichotomous, e.g. pass/fail), and no control variable, then go for t- Test.
If your categorical variable is of two levels, say true/false, then, apply t-test while ANOVA can be applied if your categorical variable is of level more than two, say, continent for an instant, i.e Europe/Asia/Africa. Nevertheless, suggested cases by @Suji Kumar Ray are still valid.
it simply depends on the nature (distribution) and the number of the variables that you are using.
From your question, you seem to have one dependent variable (which is continuous) and one independent variable (which is categorical)
Scenario 1
If the dependent variable is normally distributed and you have a categorical independent variable that has just 2 levels (dichotomous) then you use INDEPENDENT T TEST.
However, If the dependent variable is not normally distributed and you have a categorical independent variable that has just 2 levels (dichotomous) then you use MANN WHITNEY U TEST.
Scenario 2
If the dependent variable is normally distributed and you have a categorical independent variable is paired then you use a PAIRED T TEST.
However, If the dependent variable is not normally distributed and you have a categorical independent variable is paired then you use WILCOXON SIGN RANK TEST.
Scenario 3
If the dependent variable is normally distributed and you have a categorical independent variable that has 3 or more levels then you use ONE WAY ANOVA.
However, If the dependent variable is not normally distributed and you have a categorical independent variable that has 3 or more levels then you use KRUSKAL WALLIS TEST.
Scenario 4
If the dependent variable is normally distributed and you have a categorical independent variable with 3 or more repeated measures, then you use a RANOVA TEST.
However, If the dependent variable is not normally distributed and you have a categorical independent variable is paired then you use FREADMAN TEST.
Dr. M. A. Fakhro did not mention anything abut the dependent variable, therefore, I will not assume here. What if there are 2 continuous dependent variables and one dichotomous independent variable? Do we still go on with Independent Sample Test or with MANOVA?