Line of Best Fit (HSC SSCE Mathematics Standard): Quizzes

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Line of Best Fit
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What is a line of best fit?

A line approximating linear relationship

What is interpolation?

Prediction within existing data range

What is a residual?

Vertical distance from point to line

What does the least-squares line of best fit minimise?

Sum of all squared residuals

What is the formula for the gradient mm of the line of best fit?

m=r×sysxm = r \times \frac{s_y}{s_x}

What is the formula for the y-intercept cc?

c=yˉ−mxˉc = \bar{y} - m\bar{x}

Which point does the line of best fit always pass through?

(xˉ,yˉ)(\bar{x}, \bar{y})

What values can Pearson's correlation coefficient rr have?

Between −1-1 and +1+1

Why are residuals squared in the least-squares method?

So negatives don't cancel out

If r=0.9743r = 0.9743, how is the association described?

Strong positive linear association

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