Q. 25 - Elementary Statistics

Question

IMR and Life Expectancy. 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. The data are presented on the Weiss Stats CD. For part (d), predict the life expectancy of the country with an IMR of 30. 

Step-by-Step Solution

Answer

(a) The scatter plot for the given datat is:

(b) Yes, it is reasonable to find the regression line for the data because the observation are scattered around a line.

(c) The regression equation is $LE=79.4-0.354IMR$. The regression equation denotes that the life expectany is decreased as the IMR decreased.

(d) The life expectancy is $68.78$ years when the IMR is 30.

(e) The value of the correlaion coefficient $r=-0.873$ 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.

(f) The 3 potential outliers are 

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

and the influential observations are:

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

Part (a) Step 1. Given Information.

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. 

Part (a) Step 2. Construct a scatterplot.

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.

Part (a) Step 3. Output.

The MINITAB output is:

Part (b) Step 1. Reasonable to find a regression line.

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.

Part (c) Step 1. MINITAB procedure.

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.

Part (c) Step 2. MINITAB output.

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.

Part (d) Step 1. Predice the life expectancy when I M R = 30 .

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

Part (e) Step 1. Determine correlation coefficient.

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.

Part (f) Step 1. Identify the potential outliers and influential observation.

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:

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