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

Infant Death/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

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

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 from StatCrunch 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

(a) The plot is:

The regression output is:

	r²	0.504
	r	-0.710
	Std. Error	6.085
	n	46
	k	1
	Dep. Var.	Obesity %
ANOVA table
Source	SS	df	MS	F	p-value
Regression	1,652.5347	1	1,652.5347	44.63	3.37E-08
Residual	1,629.2586	44	37.0286
Total	3,281.7933	45
Regression output					confidence interval
variables	coefficients	std. error	t (df=44)	p-value	95% lower	95% upper
Intercept	26.6228
Infant Death/1000	-0.4360	0.0653	-6.680	3.37E-08	-0.5676	-0.3045

(b) The correlation coefficient (r) is -0.710.

The equation for the linear relationship is:

y = -0.436*x + 26.623

The critical value is 0.304.

(c) The hypothesis being tested is:

H₀: β₁ = 0

H₁: β₁ ≠ 0

The p-value from the output is 0.0000.

Since the p-value (0.0000) is less than the significance level (0.05), we can reject the null hypothesis.

Therefore, we can conclude that the slope is significant.

Yes, there is a valid linear relationship between obesity rates and infant mortality rates.

(d) Yes, the variables may have a cause-and-effect relationship between obesity rates and infant mortality rates.

(e) BMI