Question

Country Algeria Argentina Australia Austria Belgium Brazil Burkina Faso Canada China Colombia Denmark Ecuador Ethiopia Finland France Germany Ghana Greece Guatemala Iceland India Ireland Israel Italy Japan Kenya Lebanon Luxembourg Malta Mexico Myanmar Netherlands New Zealand Nicaragua Norway Peru Portugal Spain Sweden Switzerland Tunisia Turkey United Arab Emirates United Kingdom United States Venezuela, RB

Obesity % 23.6 26.5 29.9 20.1 22.1 20.1 5.2 30.1 7.3 20.7 21 18 3.3 22.8 25.7 22.7 10.9 25.1 16.4 23.9 4.7 27 25.8 23.7 3.5 5.9 30.8 24.8 28.7 27.6 2.9 21.9 30.6 15.5 24.8 20.4 22.1 26.5 22 21 27.1 29.4 34.5 29.8 35 24.3

Infant deaths/1000 21.9 11.1 3 2.9 3.3 14.6 60.9 4.3 9.2 13.6 2.9 18.4 41.4 1.9 3.5 3.1 42.8 3.6 24.3 1.6 37.9 3 3.2 2.9 2 36.6 7.3 1.6 5.2 11.9 40.7 4.8 3.3 19.4 2.2 13.6 3 3.6 2.4 3.5 12.1 11.6 5.9 3.5 5.6 12.9

Is there a linear relationship between the obesity rates and infant mortality for countries in the Global Health Summary data set? Investigate the relationship between obesity rates and infant mortality by using StatCrunch and complete the parts below.

1. Use the Simple Linear Regression feature in StatCrunch to construct the regression model and scatterplot to compare the obesity rate (x-variable) to the infant deaths per 1000 (y-variable). Insert the results in the space below. (TIP: You need to insert both the linear regression information and the scatterplot.)

<insert graphic here>

2. Report the correlation coefficient (r) and write the equation for the linear relationship as ____Locate the critical value for correlation coefficients with a sample size of thirty or higher. (If necessary, round your answers to the nearest hundredth.)

3. Determine if there is a valid linear relationship between obesity rates and infant mortality rates. To receive full credit, your answer should make use of the correlation coefficient and the critical value. If there is a linear relationship, describe how the two variables are related.

4. Would it be appropriate to conclude a cause-and-effect relationship between obesity rates and infant mortality rates? Explain why or why not.

5. Identify at least one confounding or lurking variable and describe how it may be related to obesity rates and infant mortality rates. (Tip: You will need to think beyond the data set for this question.)

Answer 1

Scatter Plot

Linear Regression Information:

Residuals:
Min 1Q Median 3Q Max
-30.6169 -6.5310 0.8581 6.6467 30.2463

Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 36.6587 3.9816 9.207 8.01e-12 ***
obesity_rate -1.1548 0.1729 -6.680 3.37e-08 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 9.903 on 44 degrees of freedom
Multiple R-squared: 0.5035,   Adjusted R-squared: 0.4923
F-statistic: 44.63 on 1 and 44 DF, p-value: 3.367e-08

Correlation Coefficient (r) : -0.7096099

Linear relationship equation :

(infant_deaths_per_1000) = 36.6587 - 1.1548 * (obesity_rate)

Critical Value for Correlation Coefficient with a random sample of 30 observation and significance level = 0.05 is 0.361

Determining if there is a valid linear relationship between obesity rates and infant mortality rates:

For the random 30 observations, Correlation Coefficient = r = -0.6996441

|r| = 0.6996441

since |r| > critical value for 30 random observations there is a  valid linear relationship between obesity rates and infant mortality rates. But because the correlation coefficient is negative so there is a negative linear relationship between obesity rates and infant mortality rates. From the linear relationship equation, if obesity_rate is increased by 1, then infant_deaths_per_1000 is decreased by 1.1548.

Would it be appropriate to conclude a cause-and-effect relationship between obesity rates and infant mortality rates? Explain why or why not.

No, we can't fully conclude cause-and-effect relationship between obesity rates and infant mortality rates. Being obese is considered to be unhealthy but still as obesity is increasing the mortality rate of infant is decreasing.

As there may be other confounding variables like diet, lifestyle, any medical condition that may affect the mortality rate as well.