Question

The following table gives mean daily calorie intake (all residents) and infant mortality rate (per 1000 births) for ten countries.

Country                Mean Daily Calories           Infant Mortality Rate

     Afghanistan                      1523                              154

             Austria                         3495                                 6

             Burundi                        1941                              114

            Colombia                       2678                               24

             Ethiopia                         1610                             107

            Germany                        3443                                6

              Liberia                          1640                             153

         New Zealand                     3362                                 7

             Turkey                          3429                               44

               USA                           3671                                 7

a)      Find the regression equation.

b)   Calculate the correlation coefficient, accurate to three decimal places  

c) Test the significance of the correlation coefficient with a 0.05 level of significance. Include definition of hypotheses, test statistic, p-value or critical value, decision about Ho, and conclusion.

d)      Find the best estimate for the infant mortality rate for a country with mean daily calorie intake of 2800.

Answer 1

a) the regression equation.

y=-0.065x+237.32

i.e.  Infant Mortality Rate=-0.065* Mean Daily Calories +237.32

b) the correlation coefficient=-0.941

by using CORREL command in Excel.

c) hypotheses

vs

test statistic

=-7.86

p-value =0.00005

reject H0.

conclusion.There is significant linear relationship between two variables.

d)      Find the best estimate for the infant mortality rate for a country with mean daily calorie intake of 2800.

Infant Mortality Rate=-0.065* Mean Daily Calories +237.32

=-0.065* 2800 +237.32

=55.32(per 1000 births)