Question

The table to the right gives the per capita gross national product and the per capita expenditure on defense for eight developed countries. Gross domestic product​ (GDP) is a measure of the total economic output of a country in monetary terms. Per capita GDP is the GDP averaged over every person in the country. Complete parts a though c.

Country	Per Capita GDP ($)	Per Capita Defense ($)
A	36,533	927
B	33,405	800
C	34,005	513
D	35,123	1333
E	33,908	344
F	47,258	1240
G	35,415	1023

H            45,758                          1700

A. Make a scatter diagram for the data.

A.

200005500002000GDPDefense Spending

A scatterplot with a horizontal axis labeled G D P from 20000 to 55000 in increments of 5000 and a vertical axis labeled Defense Spending from 0 to 2000 in increments of 200 contains 8 points. (37500, 900); (32500, 800); (35000, 500); (35000, 1300); (35000, 300); (47500, 1200); (35000, 1000); (45000, 1700). All coordinates are approximate.

B.

200005500002000GDPDefense Spending

A scatterplot with a horizontal axis labeled G D P from 20000 to 55000 in increments of 5000 and a vertical axis labeled Defense Spending from 0 to 2000 in increments of 200 contains 8 points. (32500, 800); (32500, 650); (35000, 600); (35000, 1450); (35000, 100); (35000, 1400); (35000, 1000); (35000, 1700). All coordinates are approximate.

C.

200005500002000GDPDefense Spending

A scatterplot with a horizontal axis labeled G D P from 20000 to 55000 in increments of 5000 and a vertical axis labeled Defense Spending from 0 to 2000 in increments of 200 contains 8 points. (37500, 1700); (32500, 500); (35000, 1000); (35000, 800); (35000, 900); (47500, 300); (35000, 1300); (45000, 1300). All coordinates are approximate.

D.

200005500002000GDPDefense Spending

State whether the two variables appear to be​ correlated, and if​ so, state whether the correlation is​ positive, negative,​ strong, or weak.

A.

The two variables appear to be correlated and the correlation is strong and positive.

B.

The two variables appear to be correlated and the correlation is weak and negative.

C.

The two variables appear to be correlated and the correlation is weak and positive.

D.

The two variables appear to be correlated and the correlation is strong and negative.

E.

The two variables do not appear to be correlated.

C. Suggest a reason for the correlation or lack of correlation.

A.

The higher a​ country's per capita​ GDP, the less it can spend on per capita national defense.

B.

The higher a​ country's per capita​ GDP, the more it can spend on per capita national defense.

C.

There is no correlation between a​ country's per capita GDP and spending on per capita national defense.

Answer 1

A.  

B.

C.

Scatter diagram for given data

By taking correlation of given data we get a value of +0.712 which means but it is not a strong correlation as the value is not nearer to one. so its a weak and positive correlation - C

From scatter plot A correlation equals +0.625 , its a weak and positive correlation -C

From scatter plot B correlation equals +0.27, its not correlated

from scatter plot C correlation equals -0.12 , its negative and very weak correlation ,

correlation defines how much does GDP depends on Defense spending and it ranges from -1 to +1 . so for given data it shows positive correlation so we can say that the higher the GDP the more it can spend on defense. also for scatter plot A.

In scatter plot B there is no any correlation as we can see that spending on defense increase for same GDP . same as in scatter plot C there is no any correlation