If you know that number ahead of time you don't need to do the experiment. If you do the experiment and it doesn't agree with the "correct" value there are 2 possible reasons. 1. You can't do the experiment properly soln: learn how to do it correctly or 2 you have discovered something. No soln except repeat the experiment enough times to determine the correct value for sure. Then publish a paper Good luck whichever path you are on. David Booth

I suggest that you trying changing the experimental settings of the input variable 'x' in your model: Y= C+ m*x

Your design matrix consists of two Columns : a vector of all ones ( n by 1) and the X vector : (x1 x2.. xn)', where xi's are the experimental values of the independent ( input) variable 'x'.

If the values of the xi's are very close to each other numerically , the X vector is close to multiple of the vector of all ones ( assuming your x variable has all numerically positive experimental values in your experimental setup), this creates a problem of ill-conditioning in the design matrix D ( n by 2) which results in an model parameter estimation issue called " Multicollinearity". I suggest you look up the issue of Multicollinearity in OLS parameter estimation situations.

In the design matrix, multicollinearity can be reduced by making the columns mutually orthogonal or close to orthogonality if possible. Statistically designed experiments choose such design points that the design matrix has mutually orthogonal columns in many cases, for example in 2^p ( p is no of input variables, or factors) factorial design experiments. In your case, I suggest you go with the Mean-centred form of the design matrix: to do this, calculate the mean value of the xi's:

xbar= (1/n) *(x1+... +xn)

Original Design matrix D= [ 1 ( n by 1) X ( n by 1) ], where X= ( x1 x2.. xn) ' , here ' denotes the vector transpose.

The mean centred design matrix E= [ 1 ( n by 1) Z ( n by 1) ], where Z = (z1 z2..... zn) ', zi= xi - xbar, I= 1,2,...,n

The difference between the original design matrix and mean centred design matrix is that while both gives the same value of the estimated slope parameter they give different values of the intercept parameter, in the mean centred design matrix the two columns are mutually orthogonal, hence, the estimated intercept parameter in this case depends only on the projection of the observation vector Y ( n by 1) in the 1 dimensional subspace: span {1 ( n by 1)} .

I suggest you look up the topic of Orthogonal polynomial regression in this context. The table of Orthogonal polynomials in context of experimental designs is available in the internet or standard texts on statistical experimental designs.... you can choose your experimental 'x' settings based on these polynomials.

As for the value of r ( or R2) less than 0.99, I suggest you do the lack-of-fit F test and test of statistical significance of your model ( at significance level alpha= 0.05 ), if the model shows no significant lack of fit and is found to be statistically significant at 95 % confidence level, your model is still acceptable one even if the R^2 is lower in magnitude, however, for these tests to be valid there are certain assumptions to be satisfied by your model: normality, lack of heteroscedasticity and uncorrelated errors, there are several graphical methods and statistical tests that can help you in testing these above mentioned model assumptions.