Which test is suitable for such data? t-test, ANOVA, linear regression? I have data in the following format:




Concentration
speed
height
distance




control
1.5
3.1
13.1


0.1
1.9
5.4
13.5


0.2
2.3
9
16.7


0.4
2.7
13.1
21.2




I am confused as to what test I should use to see if there is statistical significance in terms of speed, height, and distance as the concentration is increased. Initially I thought ANOVA was the answer as there is one categorical independent variable (the concentration, with at least three levels), and one or more quantitative dependent variables (three different ANOVAs, one for each column).
I have another set of values with the same parameters and want to compare them with this initial set too and was also wondering what test would be appropriate. The two-way ANOVA seemed to fit as I will be comparing concentration and time but I cannot get the one way ANOVA to work in the first problem.

It is not a good goal to "see if there is statistical significance".  There are many problems with the idea of "statistical significance", chief among them being dichotomous thinking that once you cross a threshold all of a sudden something is "significant".  Better to make a goal of quantifying to what degree X is related to Y.
Your particular problem is that of a single X against a multivariate Y.  Multivariate methods make a lot of assumptions, so it is good to use an approach advocated by Peter O'Brien in which you turn the problem around to try to predict the concentration simultaneously from the three response variables.  Consider concentration as ordinal and use an ordinal regression model.  From that you'll get a measure of rank correlation, a statistical test of the global null hypothesis of no association (likelihood ratio $\chi^2$ test with 3 degrees of freedom) and more.
