3 . The following table shows the temperature ( y C ) of the motor of a car travelling with speed
�1
( x ms )
.
Speed
�1
( x ms )
30 40 50 60 70 Temperature ( y C ) 98 122 137 115 100
It is assumed that the two variables follow a bivariate normal distribution with product moment correlation coefficient � . A hypothesis test is conducted at a 5 % significance level to test whether there is a positive 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 .
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( 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
� �0.1 �8 � 70.
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( f ) Write down SS res
, the sum of square residuals .
It is also given that the coefficient of determination under the new model is 0.9037 .
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( g ) By using R
SS SS
2 res �1� , find tot tot
SS , the total sum of squares . [ 2 ] www . seprodstore . com
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