91Ó°ÊÓ

IMR and Life Expectancy. From the International Data Base, published by the U.S. Census Burcau, we obtained data on infant mortality rate (IMR) and life expectancy (LE), in years, for a sample of 60 countries. The data are presented on the WeissStats site.

- For the estimations and predictions, use an IMR of 30 .

- For the correlation test, decide whether IMR and life expectancy are negatively linearly correlated.

a. defermine the sample regression equation.

b. find and inferpret the standard ernor of the estimate.

c. decide, at the 5 se sigmificance level, whether the data provide suf. ficiemt eviderte to comclude that the predicfor wariable is useful forpredicting the response variable.

d. determine and interpret a point estimate for the condifional mean of the respomse variable correspomding to the specified tahue of the predictor variable.

e. find comd inferpret a $${955}^{-}$$comfidence inferwi for the comdifiond ment of the nesponse variable correspomdins to the specifiet Walue of the predictor variable.

f. defermine curd inferpref the predicted value of the hespontie teari able corresporalime to the specified iultwe of the predictor tariable.

g. find und inferpret a $95 \%$ prediction imterval for the value of the respomse variable corresponding fo the specified valte of the predicfor variable.

h. compare and discuss the differences befueen the confidence infer. val that you obtained in part $(e)$ ard the prediction imfervi that you obtained in part $(g)$.

i. perform and inferpref the required cerrelation $t$-fest at the 5 fe significance level.

j. perform a residual andysis fo decide whether making the preceding inferences is reasomable. Explain your arswer.

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