County MEAN DAILY CALORIES INFANT MORTALITY RATE (PER 1,000 BIRTHS) 1 1,512 154
ID: 3060390 • Letter: C
Question
County
MEAN DAILY CALORIES
INFANT MORTALITY RATE (PER 1,000 BIRTHS)
1
1,512
154
2
3,484
6
3
1,930
114
4
2,667
24
5
1,599
107
6
3,432
6
7
1,629
153
8
3,418
7
9
3,418
44
10
3,660
7
Consider the following table showing mean daily caloric intake (all residents) and infant mortality rale (per 1,000 births) for 10 countries.
Compute r and r 2
R= ____ (Type an integer or decimal to two decimal places as needed)
Compute R 2
R 2=____ (Type an integer or decimal to two decimal places as needed)
For this case do you believe that the best fit line gives reliable predictions outside the range of the data on the scatter diagram?
a Pedictions based on the best fit line could be reliable because the value of r2 is sufficiently large.
b. Pedictions based on the best fit line could NOT be reliable because the value of r2 is sufficiently large
County
MEAN DAILY CALORIES
INFANT MORTALITY RATE (PER 1,000 BIRTHS)
1
1,512
154
2
3,484
6
3
1,930
114
4
2,667
24
5
1,599
107
6
3,432
6
7
1,629
153
8
3,418
7
9
3,418
44
10
3,660
7
Explanation / Answer
The statistical software output for this problem is:
Simple linear regression results:
Dependent Variable: Infant Mortality Rate
Independent Variable: Mean Daily Calories
Infant Mortality Rate = 236.12464 - 0.06502099 Mean Daily Calories
Sample size: 10
R (correlation coefficient) = -0.94180494
R-sq = 0.88699654
Estimate of error standard deviation: 22.413194
Parameter estimates:
Analysis of variance table for regression model:
Hence,
R = -0.94
R2 = 0.89
Pedictions based on the best fit line could be reliable because the value of r2 is sufficiently large.
Option A is correct.
Parameter Estimate Std. Err. Alternative DF T-Stat P-value Intercept 236.12464 23.064331 0 8 10.237654 <0.0001 Slope -0.06502099 0.0082052817 0 8 -7.9242849 <0.0001