Question

The data for per capita income and per capita alcohol consumption for

66

countries is given in the table.​ Here, x denotes​ income, in thousands of​ dollars, and y denotes alcohol​ consumed, in gallons per year. Use the information to complete parts

left parenthesis a right parenthesis through(a) through

​(d).

x	20.4	22.6	26.6	19.1	27.3	24.3
y	20.8	29.7	28.4	15.7	20.3	31.0

a. Graph the data points.

A.

1535050IncomeAlcohol

A scatterplot has a horizontal axis labeled Income from 15 to 35 in increments of 10 and a vertical axis labeled Alcohol from 0 to 50 in increments of 10. The following points are plotted: (19, 28); (20, 31); (23, 20); (24, 21); (27, 16); (27, 30). All coordinates are approximate.

B.

1535050IncomeAlcohol

A scatterplot has a horizontal axis labeled Income from 15 to 35 in increments of 10 and a vertical axis labeled Alcohol from 0 to 50 in increments of 10. The following points are plotted: (19, 16); (20, 21); (23, 30); (24, 31); (27, 28); (27, 20). All coordinates are approximate.

C.

1535050IncomeAlcohol

A scatterplot has a horizontal axis labeled Income from 15 to 35 in increments of 10 and a vertical axis labeled Alcohol from 0 to 50 in increments of 10. The following points are plotted: (19, 31); (20, 30); (23, 28); (24, 21); (27, 20); (27, 16). All coordinates are approximate.

D.

1535050IncomeAlcohol

A scatterplot has a horizontal axis labeled Income from 15 to 35 in increments of 10 and a vertical axis labeled Alcohol from 0 to 50 in increments of 10. The following points are plotted: (19, 21); (20, 28); (23, 30); (24, 31); (27, 21); (27, 20). All coordinates are approximate.

b. Decide whether finding a regression line for the data is reasonable.

A.

There is a clear nonlinear pattern to the​ data, so it is inappropriate to carry out a linear regression.

B.

There is a linear pattern to the​ data, so it is appropriate to carry out a linear regression.

C.

There is no pattern to the​ data, so it is inappropriate to carry out a linear regression.

c. Find the regression equation for the data points. Select the correct choice below and fill in any answer boxes within your choice.

A.

ModifyingAbove y with caretyequals=

​(Round to two decimal places as​ needed.)

B.

A regression line for the data is not reasonable.

d. Identify any outliers and potential influential observations.

A.

There is one outlier and no influential observations.

B.

There are no outliers and one influential observation.

C.

There are one or more outliers and influential observations.

D.

There are no outliers and no influential observations.

E.

Not applicable since a regression line for the data is not reasonable

Click to select your answer.

Answer 1

I have used R to plot the graph among x and y and the code and output is a follows

x=c(20.4,22.6,26.6,19.1,27.3,24.3)
> y=c(20.8,29.7,28.4,15.7,20.3,31)
> plot(x,y)

OUTPUT

O 30 o 25 у O 0 20 20 22 24 26 X

a) Option B

As the given points are closed to the points of option B, option B is correct.

b) Option A

As it can be clearly observed from the graph that the pattern is non-linear we can't fit a linear regression line to this, it can be observed that it is nowhere close to linear trend, initially y increases as x increase and then decreases as x increase.

c) Option B

A regression line is not reasonable.

d) Option E

As the regression line is not suitable we won't have any outlier.

Do comment if you have any doubt.

Thank you !!