Your Practice Set – Applications and Interpretation for IBDP Mathematics
3 . The performance of a football team is studied . The following table shows the number of goals scored x of the team in five matches and the number of goals conceded y in the matches .
Number of goals scored ( x ) |
1 |
2 |
1 |
2 |
3 |
Number of goals conceded ( y ) |
1 |
4 |
2 |
5 |
8 |
It is suggested that the relationship between the variables can be modelled by the regression equation
2 y � ax �bx � c , where a , b , c� .
( a ) |
( i ) |
Write down the least square regression curve for the number of goals |
|
|
conceded . |
( ii ) Write down the coefficient of determination .
( b ) Write down SS res
, the sum of square residuals .
( c ) By using R
SS SS
2 res �1� , find tot tot
SS , the total sum of squares .
[ 3 ]
[ 2 ]
[ 2 ]
4 . The relationship between the cost and the revenue of the products in a company is studied . The following table shows the cost x ( in EUR ) of the four products in the company and the corresponding revenue y ( in EUR ).
Cost ( x EUR ) 3 4 5 6 Revenue ( y EUR ) 6 8 11 15
It is suggested that the relationship between the variables can be modelled by the x regression equation y �a� b , where a , b� .
( a ) ( i ) Write down the least square regression curve for the revenue of products .
( ii ) Write down the coefficient of determination , giving the answer in five decimal places .
( b ) Write down SS res
, the sum of square residuals .
( c ) By using R
SS SS
2 res �1� , find tot tot
SS , the total sum of squares .
[ 3 ]
[ 2 ]
[ 2 ]
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