Q.4.115 - Elementary Statistics

Question

 Estriol Level and Birth Weight. J. Greene and J. Touchstone conducted a study on the relationship between the estriol levels of pregnant women and the birth weights of their children. Their findings. "Urinary Tract Estriol: An Index of Placental Function," were published in the American lournal of obstetrics and Gynecology (Vol. 85(1). pp. 1-9). The data from the study are provided on the WeissStats site, where estriol levels are in $mg/24 hr$ birth weights are in hectograms.

a. Decide whether finding a regression line for the data is reasonable. If so, then also do parts (b) (d).

b. Obtain the coefficient of determination.

c. Determine the percentage of variation in the observed values of the response variable explained by the regression. and interpret your answer.

d. State how useful the regression equation appears to be for making predictions.

Step-by-Step Solution

Answer

(a)  Finding a regression line for the data is reasonable .

(b) The coefficient of determination is $0.3718$

(c) Percentage of variation is $37.18\%$

(d) The regression equation is not useful for making predictions.

Part (a) Step 1: Given Information

Estriol Level and Birth Weight. J. Greene and J. Touchstone conducted a study on the relationship between the estriol levels of pregnant women and the birth weights of their children. Their findings. "Urinary Tract Estriol: An Index of Placental Function," were published in the American lournal of obstetrics and Gynecology (Vol. 85(1). pp. 1-9). The data from the study are provided on the WeissStats site, where estriol levels are in $mg/24 hr$ birth weights are in hectograms. 

We have to decide  whether finding a regression line for the data is reasonable. If so, then also do parts (b) (d). 

Part (a) Step 2: Explanation

The MINITAB: can be used to create a scatterplot for the given data.

Step 1: to Graph > Scatterplot.

Step 2: Click OK after selecting With Connect Line.

Step 3: Add a WEIGHT column to the $Y$ variables section.

Step 4: Add an ESTRIOL column to the $X$variables.

Step 5: Click the OK button.

The resulting scatterplot will be

Because the observations are dispersed around a line in the scatterplot above, it is reasonable to find a regression line for the data.

Part (b) Step 1: Given Information

Estriol Level and Birth Weight. J. Greene and J. Touchstone conducted a study on the relationship between the estriol levels of pregnant women and the birth weights of their children. Their findings. "Urinary Tract Estriol: An Index of Placental Function," were published in the American lournal of obstetrics and Gynecology (Vol. 85(1). pp. 1-9). The data from the study are provided on the WeissStats site, where estriol levels are in $mg/24hr$ birth weights are in hectograms. we have to determine the coefficient of determination. 

Part (b) Step 2: Explanation

MINITAB can be used to calculate the coefficient of determination as follows:

Step 1: go to Stat > Regression > Regression.

Step 2: In the Response column, type WEIGHT.

Step 3: In Predictors, add the ESTRIOL column.

Step 4: Click the OK button.

MINITAB's output will be as follows:

Therefore the coefficient of determination is $0.3718$ 

Part (c) Step 1: Given Information

 Estriol Level and Birth Weight. J. Greene and J. Touchstone conducted a study on the relationship between the estriol levels of pregnant women and the birth weights of their children. Their findings. "Urinary Tract Estriol: An Index of Placental Function," were published in the American lournal of obstetrics and Gynecology (Vol. 85(1). pp. 1-9). The data from the study are provided on the WeissStats site, where estriol levels are in $mg/24 hr$ birth weights are in hectograms. we have to determine the percentage of variation in the observed values of the response variable explained by the regression .

Part (c) Step 2: Explanation

The coefficient of determination will be $0.3718$

As a result, the regression explains $37.18\%$t of the variation in the observed values of the response variable. It can be deduced that the linear association between Estriol level $\left(x\right)$ and birth weight accounts for $37.18\%$ of the variability in birth weight $\left(y\right)$.

Part (d) Step 1: Given Information

 Estriol Level and Birth Weight. J. Greene and J. Touchstone conducted a study on the relationship between the estriol levels of pregnant women and the birth weights of their children. Their findings. "Urinary Tract Estriol: An Index of Placental Function," were published in the American lournal of obstetrics and Gynecology (Vol. 85(1). pp. 1-9). The data from the study are provided on the WeissStats site, where estriol levels are in $mg/24hr$ birth weights are in hectograms. we have to state how useful the regression equation appears to be for making predictions. 

Part (d) Step 2: Explanation

The coefficient of determination will be $0.3718$

As a result, the regression explains $37.18\%$ of the variation in the observed values of the response variable. It can be deduced that the linear association between Estriol level $\left(x\right)$ and birth weight accounts for$37.18\%$ of the variability in birth weight $\left(y\right)$

Because the proportion of variance in the observed values of the response variable explained by the regression is less than $50$ percent, the regression equation is not useful in making predictions.