91Ó°ÊÓ

From the International Data Base, published by the U.S. Census Bureau, we obtained data on infant mortality rate (IMR) and life expectancy (LE), in years, for a sample of 60 countries.

Construct a scatter plot by using MINITAB.

1. Choose Graph > Scatterplot.

2. Choose Connect Line > OK.

3. Under Y-variables, enter column of LE.

4. Under X-variables, enter the colum of IMR.

5. Click OK.

The MINITAB output is:

To find if it is reasonable to find a regression line.

Yes, it is reasonable to find the regression line for the data because the observation are scattered around a line. There are no outlier and an influential observation.

Find the regression equation by using MINITAB procedure.

1. Choose Stat > Regression > Regression.

2. In response enter the column LE.

3. In predictor, enter the columns of IMR.

4. Click OK.

The MINITAB output is:

Regression analyis: LE versus IMR.

From the output, the regression equaton is$LE=79.4-0.354IMR$.

The regression equation denotes that the life expectany is decreased as the IMR decreased.

$$\begin{gathered} LE=79.4-0.354\left(30\right) \\ =79.4-10.62 \\ =68.78years \end{gathered}$$

By using MINITAB procedure, the correlation coefficient is $r=-0.873$.

The value of the correlaion coefficient indicates that there is a strong relation between LE and IMR. And the slope of the regression line is negative because the correlation value is negative.

From MINITAB output in part (A), there are 3 potential outliers:

$$\begin{gathered} IMR=46;LE=49.89 \\ IMR=34;LE=44.28 \\ IMR=44;LE=50.16 \end{gathered}$$

There are 2 influential observation. They are:

$$\begin{gathered} IMR=100;LE=47.43 \\ IMR=91;LE=43.45 \end{gathered}$$