Fitting a Linear Model to the Data (VCE SSCE General Mathematics): Flashcards

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Fitting a Linear Model to the Data
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Linear regression definition

Process of fitting a straight line to data

In y=a+bxy = a + bx, what is aa?

yy-intercept

In y=a+bxy = a + bx, what is bb?

Slope

What is fitting by eye?

Visual method using ruler to draw line balancing data points

Slope formula using two points

b=y2y1x2x1b = \frac{y_2 - y_1}{x_2 - x_1}

What is a residual?

Vertical distance between data point and fitted line

When is a residual positive?

When data point lies above the line

What does least squares method minimize?

Sum of squared residuals

Slope formula for least squares line

b=rsysxb = r \frac{s_y}{s_x}

Intercept formula for least squares line

a=yˉbxˉa = \bar{y} - b\bar{x}

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