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Question Six The table below gives the numbers of deaths $n_x$ in a year in groups of women aged $x$ years. The exposures of the groups, denoted $E_x$, are also given (the exposure is essentially the number of women alive for the year in question). The values of the death rates $y_x$, where $y_x = n_x/E_x$, and the log(death rates), denoted $w_x$, are also given. age $x$ number of deaths $n_x$ exposure $E_x$ $y_x = n_x/E_x$ $w_x = log y_x$ 70 30 426 0.07042 -2.6532 71 38 471 0.08068 -2.5173 72 38 454 0.08370 -2.4805 73 53 482 0.10996 -2.2077 74 59 445 0.13258 -2.0205 75 61 423 0.14421 -1.9365 76 82 468 0.17521 -1.7417 77 96 430 0.22326 -1.4994 $\sum x = 588$ $\sum x^2 = 43260$ $\sum w = -17.0568$ $\sum w^2 = 37.5173$ $\sum xw = -1246.7879$vate Windov Settings to activ (i) A scatter plot of $y_x$ against $x$ is shown below. 0.25 0.20 0.15- 0.10 0.05 0.00 69 70 71 72 73 74 75 76 77 78 Draw a scatter plot of $w_x$ against $x$ and comment briefly on the two scattere Windov plots and the relationships displayed. Go to Settin [3] act (ii) (a) Calculate the least squares fit regression line in which $w_x$ is modelled as the response and $x$ as the explanatory variable. (b) Draw the fitted line on your scatter plot of $w_x$ against $x$. (c) Calculate a 95% confidence interval for the slope coefficient of the regression model of $w_x$ on $x$, adopting the assumptions of the usual "normal regression model". (d) Calculate the fitted values for the number of deaths for the group aged 71 years and the group aged 76 years. [12] (Ⅲ) Explain briefly the relationship between the fitting procedure used in part (ii) and a model which states that the number of deaths $N_x$ is a random variable with mean $E_x b c^x$ for some constants $b$ and $c$. [3]

          Question Six
The table below gives the numbers of deaths $n_x$ in a year in groups of women aged $x$
years. The exposures of the groups, denoted $E_x$, are also given (the exposure is
essentially the number of women alive for the year in question). The values of the
death rates $y_x$, where $y_x = n_x/E_x$, and the log(death rates), denoted $w_x$, are also given.
age $x$ number of deaths $n_x$ exposure $E_x$
$y_x = n_x/E_x$
$w_x = log y_x$
70
30
426
0.07042
-2.6532
71
38
471
0.08068
-2.5173
72
38
454
0.08370
-2.4805
73
53
482
0.10996
-2.2077
74
59
445
0.13258
-2.0205
75
61
423
0.14421
-1.9365
76
82
468
0.17521
-1.7417
77
96
430
0.22326
-1.4994
$\sum x = 588$ $\sum x^2 = 43260$ $\sum w = -17.0568$ $\sum w^2 = 37.5173$ $\sum xw = -1246.7879$vate Windov
Settings to activ
(i)
A scatter plot of $y_x$ against $x$ is shown below.
0.25
0.20
0.15-
0.10
0.05
0.00
69 70 71 72 73 74 75 76 77 78
Draw a scatter plot of $w_x$ against $x$ and comment briefly on the two scattere Windov
plots and the relationships displayed.
Go to Settin [3] act
(ii)
(a)
Calculate the least squares fit regression line in which $w_x$ is modelled
as the response and $x$ as the explanatory variable.
(b)
Draw the fitted line on your scatter plot of $w_x$ against $x$.
(c)
Calculate a 95% confidence interval for the slope coefficient of the
regression model of $w_x$ on $x$, adopting the assumptions of the usual
"normal regression model".
(d)
Calculate the fitted values for the number of deaths for the group aged
71 years and the group aged 76 years.
[12]
(Ⅲ)
Explain briefly the relationship between the fitting procedure used in part (ii)
and a model which states that the number of deaths $N_x$ is a random variable
with mean $E_x b c^x$ for some constants $b$ and $c$.
[3]

question six the table below gives the numbers of deaths nx in a year in groups of women aged x years the exposures of the groups denoted ex are also given the exposure is essentially the 29316

Added by Scott S.

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