Question

9. You are an actuarial student working for a large life insurance company in India. Appointed [4] Actuary has asked you to analyse the claims data to understand the impact of age on number of COVID claims. You have received the following information from claims depatment. \begin{tabular}{|c|c|} \hline Age(X) & Number of COVID claims per 10,000 policies(Y) \\ \hline 5 & 101 \\ \hline 15 & 120 \\ \hline 25 & 135 \\ \hline 35 & 186 \\ \hline 45 & 268 \\ \hline 55 & 540 \\ \hline 65 & 620 \\ \hline \end{tabular} \[ \Sigma\left(\mathrm{x}_{\mathrm{i}}-\mathrm{x}\right)^{2}=2.800 \quad \sum\left(\mathrm{y}_{\mathrm{i}}-\bar{y}\right)^{2}=2,70,832 \quad \Sigma\left(\left(\mathrm{x}_{\mathrm{i}}-\mathrm{x}\right)\left(\mathrm{y}_{\mathrm{i}}-\overline{\mathrm{y}}\right)\right)=25,300 \] You have been asked to perform linear regression analysis on the data to identify the relationship between age and number of COVID claims. ALMinus 43, Mall Rond Gatii Nagan, S/F, Dehive os999. 50.930 .99991900 infoltalphaplusdelhimom, Bation aliphaphselh 14 ALPHAPLUS \( \operatorname{csin} \) (Actuatial Science) i) Determine the fitted regression line with 'no. of claims' as the response and 'age' as the (3) explanatory variable. ii) Assuming the full normal model. caletiate the estimate of the error variance \( \sigma^{2} \) and (3) obtain a \( 90 \% \) confidence interval for \( \sigma^{2} \). iii) Calculate the proportion of variance explained by the model. Hence, comment on the (3) fit of the model. iv) By considering the slope parameter, formally test whether the data is positively (3) correlated. 1) Calculate \( 95 \% \) confidence interval for mean predicted number of COVID claims (4) corresponding to age of 60 . vi) Assess the fitness of the model by: a) Completing the table of residuals (nearest rounded number) \begin{tabular}{|l|c|c|c|c|c|c|c|} \hline Age & 5 & 15 & 25 & 35 & 45 & 55 & 65 \\ \hline Residual & 91 & & -56 & -95 & & 78 & \\ \hline \end{tabular} (2) b) Comment on appropriateness of linear model. (3)

          9. You are an actuarial student working for a large life insurance company in India. Appointed
[4]
Actuary has asked you to analyse the claims data to understand the impact of age on number of COVID claims. You have received the following information from claims depatment.
\begin{tabular}{|c|c|}
\hline Age(X) & Number of COVID claims per 10,000 policies(Y) \\
\hline 5 & 101 \\
\hline 15 & 120 \\
\hline 25 & 135 \\
\hline 35 & 186 \\
\hline 45 & 268 \\
\hline 55 & 540 \\
\hline 65 & 620 \\
\hline
\end{tabular}
\[
\Sigma\left(\mathrm{x}_{\mathrm{i}}-\mathrm{x}\right)^{2}=2.800 \quad \sum\left(\mathrm{y}_{\mathrm{i}}-\bar{y}\right)^{2}=2,70,832 \quad \Sigma\left(\left(\mathrm{x}_{\mathrm{i}}-\mathrm{x}\right)\left(\mathrm{y}_{\mathrm{i}}-\overline{\mathrm{y}}\right)\right)=25,300
\]

You have been asked to perform linear regression analysis on the data to identify the relationship between age and number of COVID claims.
ALMinus 43, Mall Rond Gatii Nagan, S/F, Dehive
os999. 50.930 .99991900
infoltalphaplusdelhimom,
Bation aliphaphselh
14

ALPHAPLUS
\( \operatorname{csin} \) (Actuatial Science)
i) Determine the fitted regression line with 'no. of claims' as the response and 'age' as the
(3)
explanatory variable.
ii) Assuming the full normal model. caletiate the estimate of the error variance \( \sigma^{2} \) and
(3)
obtain a \( 90 \% \) confidence interval for \( \sigma^{2} \).
iii) Calculate the proportion of variance explained by the model. Hence, comment on the
(3)
fit of the model.
iv) By considering the slope parameter, formally test whether the data is positively
(3)
correlated.
1) Calculate \( 95 \% \) confidence interval for mean predicted number of COVID claims
(4)
corresponding to age of 60 .
vi) Assess the fitness of the model by:
a) Completing the table of residuals (nearest rounded number)
\begin{tabular}{|l|c|c|c|c|c|c|c|}
\hline Age & 5 & 15 & 25 & 35 & 45 & 55 & 65 \\
\hline Residual & 91 & & -56 & -95 & & 78 & \\
\hline
\end{tabular}
(2)
b) Comment on appropriateness of linear model.
(3)

9. You are an actuarial student working for a large life insurance company in India. Appointed
[4]
Actuary has asked you to analyse the claims data to understand the impact of age on number of COVID claims. You have received the following information from claims depatment.

Age(X) Number of COVID claims per 10,000 policies(Y)

5 101

15 120

25 135

35 186

45 268

55 540

65 620

Σ(xi-x)^2=2.800 ∑(yi-y̅)^2=2,70,832 Σ((xi-x)(yi-y))=25,300

You have been asked to perform linear regression analysis on the data to identify the relationship between age and number of COVID claims.
ALMinus 43, Mall Rond Gatii Nagan, S/F, Dehive
os999. 50.930 .99991900
infoltalphaplusdelhimom,
Bation aliphaphselh
14

ALPHAPLUS
csin (Actuatial Science)
i) Determine the fitted regression line with 'no. of claims' as the response and 'age' as the
(3)
explanatory variable.
ii) Assuming the full normal model. caletiate the estimate of the error variance σ^2 and
(3)
obtain a 90 % confidence interval for σ^2.
iii) Calculate the proportion of variance explained by the model. Hence, comment on the
(3)
fit of the model.
iv) By considering the slope parameter, formally test whether the data is positively
(3)
correlated.
1) Calculate 95 % confidence interval for mean predicted number of COVID claims
(4)
corresponding to age of 60 .
vi) Assess the fitness of the model by:
a) Completing the table of residuals (nearest rounded number)

Age 5 15 25 35 45 55 65

Residual 91 -56 -95 78

(2)
b) Comment on appropriateness of linear model.
(3)

Added by Celia N.

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