Q. 4.165 - Elementary Statistics

Question

Estriol Level and Birth Weight. The data for estriol levels of pregnant women and birth weights of their children from Exercise $4.115$ are on the Weiss $5$ tats site.

a. Decide whether use of the linear correlation coefficient as a descriptive measure for the data is appropriate, If so, then also parts  $\left(b\right)$ and $\left(c\right)$.

b. Obtain the linear correlation coefficient.

c. Interpret the value of $r$ in terms of the linear relationship between the two variables in question.

Step-by-Step Solution

Answer

(a) As a descriptive metric for the data, the linear correlation coefficient is acceptable.

(b) The linear correlation coefficient is $0.610$.

(c) It shows that the variables age and $\%$ fat have a moderately favorable linear relationship.

Part (a) Step 1: Given Information

Whether the use of linear correlation coefficient is appropriate or not.

Part (a) Step 2: Explanation

The scatterplot for the given data can be drawn by using the MINITAB:

Step 1: Choose Graph $>$Scatterplot.

Step 2: Choose With Connect Line, and then click OK.

Step 3: Under $Y$ variables, enter a column of WEIGHT.

Step 4: Under $X$ variables, enter a column of ESTRIOL.

Step 5: Click OK.

Part (a) Step 3: Explanation

The scatterplot obtained will be,

Because the observations are spread around a line in the scatterplot above, it is fair to establish a regression line for the data.

Part (b) Step 4: Given Information

The linear correlation coefficient.

Part (b) Step 5: Explanation

The linear correlation coefficient can be obtained by using MINITAB as follows:

Step 1: Choose Stat >Basic Statistics > Correlation

Step 2: In Variables, select Estrioland Weight from the box on the left

Step 3: Click OK.

The MINITAB output will be:

MINITAB procedure:

Step 1: Select Stat >Basic Statistics > Correlation.

Step 2: In Variables, select Estriol and Weight from the box on the left.

Step 3: Click OK.

Hence, the linear correlation coefficient will be $0.610$.

Part (c) Step 6: Given Information

The interpretation of the value of linear correlation coefficient.

Part (c) Step 7: Explanation

The linear correlation coefficient will be $0.610$ which is neither close nor far from 1.

It shows that the variables weight and Estriol have a somewhat favorable linear relationship.

If the value of $x$ increases, then the corresponding value of $y$ increases.

In other words, the smaller value of $x$ is related with the smaller value of $y$ or the larger value of $x$is related to the larger value of $y$.

Furthermore, because the correlation value is positive, the slope of the regression line is positive.

It shows that the variables age and % fat have a moderately favorable linear relationship.