2 . The following table shows the age of a silver coin x ( in years ) and the corresponding pure weight y ( in g ).
Age of a silver coin ( x years ) 13 16 19 23 28 Pure weight ( y g ) 6 7 5 4.8 4.6
( a ) The relationship between the variables is modelled by the regression equation y �ax � b .
( i ) Write down the value of a and of b .
( ii ) Hence , estimate the pure weight of a silver coin when it is a quarter-century old .
( b ) ( i ) Write down the correlation coefficient .
[ 4 ]
( ii ) Write down the coefficient of determination .
( iii ) Hence , interpret the coefficient of determination . [ 3 ]
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3 . The expenditures of a group of market customers are studied . The following table shows the times x ( in minutes ) of six customers spent in a market and their corresponding expenditures y ( in USD ).
Time spent ( x minutes ) 47 28 35 7 11 50 Expenditure ( y USD ) 50 50 42 16 5 15
( a ) The relationship between the variables is modelled by the regression equation y �ax � b .
( i ) Write down the value of a and of b .
( ii ) Explain what the gradient a represents .
( b ) ( i ) Write down the correlation coefficient .
[ 3 ]
( ii ) Write down the coefficient of determination .
( iii ) Hence , interpret the coefficient of determination . [ 3 ]
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