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Advanced Higher

STATISTICS. Advanced Higher. Linear Regression.

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Advanced Higher

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  1. STATISTICS Advanced Higher Linear Regression To see if there is a relationship between two variables, we draw a scatter-graph. It is then possible to draw a ‘best-fit’ line through the points on the graph. To draw the straight line, we try to have as many points as possible on either side of the line. This is pretty difficult so we calculate a line of regression instead: this is called linear regression.

  2. STATISTICS Advanced Higher The formula for drawing the linear regression The equation for a straight line is Y = a + bX • ‘a’ is known as the ‘intercept’. • It is given by the formula: a = ӯ - bẊ • ‘b’ is the ‘regression coefficient’ • It is given by the formula: b = ∑(Ẋ-X)(y-ӯ) ∑(X-Ẋ)2

  3. STATISTICS Advanced Higher First: draw yourself a scatter-graph to show the relationship between two variables Scatter graph showing the relationship between discharge and suspended on the River Farg Increasing suspended load Increasing river discharge

  4. STATISTICS Advanced Higher Second: complete Pearsons Product to get the values you need for ‘b’ • b = ∑(Ẋ-X)(y-ӯ) ∑(X-Ẋ)2

  5. STATISTICS Advanced Higher Second: complete Pearsons Product to get the values you need for ‘b’ • b = ∑(Ẋ-X)(y-ӯ) ∑(X-Ẋ)2 • b = 4.65 0.62 • b = 7.5

  6. STATISTICS Advanced Higher Third: calculate ‘a’ using the formula • a = ӯ - bẊ • a = ӯ - bẊ • a = 12.44 – (7.5 x 0.723) • a = 7.02

  7. STATISTICS Advanced Higher Fourth: figure out some ‘x’ & ‘y’ values • To draw the straight line you have to calculate the values of ‘y’ for values of ‘x’ that you choose. • For example, if x = 0, then y = a + (b x 0) • For example, if x = 20, then y = a + (b x 20) • a = 7.02 • b = 7.5 • To draw the straight line you have to calculate the • values of ‘y’ for values of ‘x’ that you choose. • if x = 0, then y = 7.02 + (7.5 x 0) = 7.02 • if x = 0.6, then y = 7.02 + (7.5 x 0.6) = 11.52 • if x = 1.2, then y = 7.02 + (7.5 x 1.2) = 16.02 • if x = 0, y = 7.02 • if x = 0.6, y = 11.52 • if x = 1.2, y = 16.02

  8. STATISTICS Advanced Higher Fifth: plot your straight line! • if x = 0, y = 7.02 • if x = 0.6, y = 11.52 • if x = 1.2, y = 16.02

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