Your Practice Set – Applications and Interpretation for IBDP Mathematics
4 . The following table shows the amount of calories ( y kcal ) of a particular kind of drinks of 250 mL containing sugar of amount ( x g ) .
Amount of sugar ( x g ) 3 6 9 12 15 Amount of calories ( y kcal ) 120 115 112 100 115
It is assumed that the two variables follow a bivariate normal distribution with product moment correlation coefficient � . A hypothesis test is conducted at a 10 % significance level to test whether there is a negative correlation between the two variables .
( a ) ( i ) Write down the null hypothesis of the test .
( ii ) Write down the alternative hypothesis of the test .
( b ) Find the p -value .
( c ) State the conclusion of the test with a reason .
This data is suggested to be modelled by the regression line with equation y �ax � b .
[ 2 ]
[ 2 ]
[ 2 ]
( d ) |
Is this suggestion a valid approach ? Explain your answer . |
( e ) |
( i ) |
Write down the coefficient of determination . |
|
( ii ) |
Hence , interpret the coefficient of determination . |
It is suggested that the relationship between the variables can be modelled by the new |
regression equation y � x � x � .
2
0.25 5 135
[ 2 ]
[ 2 ]
( f ) Write down the exact value of SS res
, the sum of square residuals .
It is also given that the coefficient of determination under the new model is 0.58 .
[ 2 ]
( g ) By using R
SS SS
2 res �1� , find tot tot
SS , the total sum of squares . [ 2 ]
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