Part II – Models for the Population 2
The following table shows the number of goals y scored by Thiago in the football league each year , where n is the number of years after 2011 :
n |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
y |
12 |
8 |
7 |
18 |
23 |
26 |
22 |
17 |
( c ) The relationship between the variables is modelled by the regression equation
3 2 y( n) an bn cn d � � � � .
( 1 ) Write down the equation of the least square regression curve , giving the coefficients correct to 6 significant figures if necessary .
( 2 ) Write down the coefficient of determination .
( 3 ) Hence , interpret the coefficient of determination .
Thiago ’ s personal trainer would like to conduct a
2
� goodness of fit test at a 10 % significance level to determine if the actual number of goals can be modelled by the following distribution :
n |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
Expected frequency |
14 |
14 |
14 |
14 |
21 |
21 |
21 |
14 |
20
( d ) ( 1 ) Write down the degree of freedom of the test .
2
( 2 ) Find the value of � calc
, the test statistic .
The critical value is given by 12.017 .
( 3 ) State the conclusion of the test with a reason .
www . seprodstore . com
307