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A visual inspection of the scatterplot should tell you whether a straight line or a simple curve is appropriate. You could carry out an analysis of variance (ANOVA) and test the reduction in the residual sums of squares to see whether the curve is significantly better than the line. However, remember that with n observations, a curve with n-1 independent parameters (for example a polynomial of order n-1) will give a prefect fit.

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Q: How do you know when to draw a curve or straight line when drawing a line of best fit?
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