Rounding in the method of least squares for linear regression analysis?

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I tend to round off the intermediate values (like that for $\Sigma x^2) $ of my calculation for slope, etc., to appropriate significant digits by considering the significance of the raw data. Sometimes I get the wrong answer because of this.

My question: Am I wrong for rounding off, or is the exercise book wrong?

Just to clarify: this is for physics data.