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EDEXCEL GCE Statistics 1

(Summary of Chapters 7)

Regression

General equation of a straight line graph

y = mx + c

General equation of a regression line

Regression analysis is most often used for prediction.

The goal in regression analysis is to create a mathematical model that can be used to

predict the values of a dependent variable based upon the values of an independent

variable.

In other words, we use the model to predict the value of Y when we know the value of

X.

The equation of the regression line of y on x is:

y = a + bx

b = Sxy

Sxx

a = y bx

If coding is done in finding out the regression equation, then decoding is necessary. To

decode, substitute the coding equations in the regression line.

for example:

Data is coded using formula: x = 10c and y = m - 700

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The regression line for code data (regression line of y on x) is : y = 36.216 4.048x

Find the equation of the regression line of m on c.

m 700 = 36.216 4.08 (10c) -------------------> m = 881.08 202.4c

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Response variable

or the dependant

variable Explanatory variable

or the independent

variable

y - intercept

gradient

which simplifies to

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Interpolation and Extrapolation

Interpolation - Finding the y-value for an x-value which is within the range of

experimental data.

Extrapolation - Finding the y-value for an x-value which is not within the range of

experimental data.

Therefore, we cannot be so sure of the value we get for y, as we dont know whether

the same pattern is held true beyond the experimented data.

Hence, extrapolation should be minimised or avoided.