Question

#1) 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

1. Calculate the correlation coefficient.

2. Is there a significant correlation between mean calorie intake and infant mortality? Conduct an appropriate test (using a significance level of a = .05) to justify your answer.

3. Find the regression equation relating Infant Mortality rate to mean calorie intake.

4. Use the regression equation to estimate the infant mortality rate for a country with mean daily calorie intake of 2800.

Answer 1

SOLUTION-

WE USE MINITAB-16 FOR COMPUTATIONS.

1.) TO FIND CORRELATION COEFFICIENT:

ENTER THE DATA> STAT> BASIC STATISTICS> CORRELATION> SELECT THE VARIABLES> OK

THE CORRELATION COEFFICIENT(r) = -0.941

2.) TO TEST SIGNIFICANCE OF CORRELATION COEFFICIENT:

THE HYPOTHESIS WE SET AS PER THE CLAIM,

[CLAIM]

THE TEST STATISTIC IS GIVEN AS,

OR,

THE CORRESPONDING P-VALUE IS < 0.00001

SO THE RESULT IS SIGNIFICANT AT 5%. HENCE THERE EXISTS A LINEAR RELATIONSHIP AMONG THE VARIABLES.

3.) TO FIND REGRESSION EQUATION:

STAT> REGRESSION> REGRESSION> SET IMR AS RESPONSE AND MEAN DAILY CALORIE AS PREDICTOR> OK

IF IMR IS Y AND MEAN DAILY CALORIE IS X, THEN THE REGRESSION EQUATION IS

4.) TO FIND THE PREDICTED INFANT MORTALITY RATE:

GIVEN, MEAN DAILY CALORIE(X)= 2800

Y= 237 - (2800*0.0654)

= 53.88

****IN CASE OF DOUBT, COMMENT BELOW. ALSO LIKE THE SOLUTION, IF POSSIBLE.