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Paper 1 – Sum of Square Residuals

Example

The distances travelled of a group of buses are studied . The following table shows the distances travelled x ( in km ) of five buses and the corresponding amounts of fuel required y ( in L ).

Distance travelled ( x km ) 100 105 140 153 180 Amount of fuel required ( y L ) 32 38 46 50 60

It is suggested that the relationship between the variables can be modelled by the regression equation y�0.3x� 2.

( a ) Use the suggested model to write down the estimated amount of fuel required when a bus is travelled by

( i ) 100 km ;

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( ii ) 105 km ;

( iii ) 153 km .

( b ) Hence , calculate SS res

, the sum of square residuals .

It is given that the coefficient of determination of this model is 0.976 .

( c ) Interpret the coefficient of determination .

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Solution

( a ) ( i ) 32 L A1

( ii ) 33.5 L A1

( iii ) 42.5 L A1

[ 3 ] www . seprodstore . com

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