1 . The insurance cost of an electric car depends partly on the distance it has travelled . The following table shows the distance and the insurance costs for five electric cars on 1 January 2021 .
|
Travelling distance ( x km
)
|
20000 |
25000 |
30000 |
35000 |
40000 |
Insurance cost ($ y ) |
12000 |
10800 |
9600 |
9000 |
8500 |
The relationship between x and y can be modelled by the regression equation y �ax � b .
( a ) By considering the above data , write down
( i ) x , the mean travelling distance ;
( ii ) y , the mean insurance cost ;
( iii ) a ;
( iv ) b ;
( v ) r , the correlation coefficient .
On 1 January 2021 , Hyung Sik buys an electric car which has travelled 32500 km .
[ 6 ]
( b ) Use the regression equation to estimate the insurance cost of Hyung Sik ’ s electric car .
[ 2 ]
On the same date , Jeong Ho buys an electric car which has travelled 52500 km .
( c ) State the reason why it is not valid to use the above regression model to estimate the insurance cost of Jeong Ho ’ s electric car .
[ 1 ]
Jeong Ho claims that the distribution of the insurance cost is expected to be as follows :
Observed insurance cost 12000 10800 9600 9000 8500 Expected insurance cost 12000 10700 9700 8800 8400
A
2
� goodness of fit test is conducted at a 5 % significance level for testing Jeong Ho ’ s claim .
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