The phrase "a linear relationship for" is correct and usable in written English.
It can be used when discussing the correlation or connection between two variables in a mathematical or statistical context.
Example: "The study found a linear relationship for the variables of temperature and pressure in the given experiment."
Alternatives: "a linear correlation for" or "a linear association for".
The test for possible non-linear relationships between the SDQ scores and the dependent variable (time to receiving health-related benefits) showed that there were no significant deviations from a linear relationship for any genders (p for non-linearity ≥0.157).
The qu and G0 exhibits a linear relationship for the curing time.
The sensor has been verified as an optical detector measuring absorbance at 420 nm, due to ferricyanide, with a linear relationship for molar concentrations of between 10−5 and 10−3, with dispersions in the measurements of less than 1%.
True precipitation potentials computed thereby show a linear relationship (for each set of halides) with (i) lattice energy; (ii) ratio of ionic radii of cation and anion; and (iii) ratio of real hydration energies of cation and anion.
A piecewise model comprised of a linear relationship for low ethanol volume fractions and a log-linear model for higher concentrations was fit to data for a surrogate gasoline comprised of eight compounds and was then used to predict BTEX concentrations in the aqueous phase equilibrated with three different commercial gasolines.
The model assumes a linear relationship for each logit as in (4).
A slope was deduced from a linear relationship established for chemical shift cf temperature pattern for each hydrogen from the amide groups (−ΔδHN/ΔT, ppm/K).
Assuming a linear relationship, and for the geometry at RB1 and RB2, we have uplift force U = −144.2d kN m−1 + 197.4 kN, and for a thickness d = 0.1 m, the uplift force is 183 kN.
A linear relationship was found for the trace element content of the raw coal (Cm) and for the different macerals and minerals (Cmi).
A linear relationship was derived for the dioxygen reduction peak potential and the decomposition rate constant.
Since the orographic effect is dominant in the explanation of precipitations in mountains, a linear relationship is considered for each pixel to connect precipitation to elevation.
