Answer the following questions based on the data below:-
X
2.9
1.2
2.1
2.6
3.5
0.9
2.8
0.6
3.2
0.8
y
2.8
0.3
1.7
2.5
3.7
-0.1
2.6
-0.5
3.4
-0.3
(a) Calculate the following statistics:-
$\sum x$, $\sum y$, $\sum x^2$, $\sum y^2$, $\sum xy$.
[6 marks]
(b) At $\alpha = 0.05$, test on the validity of null hypothesis of equal mean between x and y. Assume
equal variance between x and y.
[12 marks]
(c) If the null hypothesis of equal variance between x and y is true,
(i)
Calculate the ratio of the variance of y and x.
(ii)
Determine the distribution of (c) (i).
[3 marks]
(d) At $\alpha = 0.05$, test on the validity of null hypothesis of no difference between x and y.
[9 marks]
(e) Let the relationship between x and y be defined as follows:-
y = $\beta_0 + \beta_1 x + \epsilon$
where, $\beta_0$ and $\beta_1$ are coefficients, and $\epsilon$ is error term distributed as Normal with mean zero and
equal variance for all observations.
(i)
Estimate $\beta_0$ and $\beta_1$.
(ii) Calculate coefficient of determination of the model, $R^2$.
[6 marks]
