Chapter 2, Problem 171E

(a)

To determine

To graph: A scatterplot of the data with 5 fruits and vegetables per day and EdCollege.

Explanation of Solution

Given: The data of people who regularly eat five or more serving of fruits and vegetables (FruitVeg5) and people earning a college degree (EdCollege) is provided in the below table.

State	EdCollege	FruitVeg5
Alabama	19.7	20.3
Alaska	23.7	23.4
Arizona	23.7	24.1
Arkansas	17.4	20.4
California	27.0	27.7
Colorado	32.6	24.8
Connecticut	32.5	28.3
Delaware	25.3	25.0
District of Columbia	45.2	31.5
Florida	23.8	24.4
Georgia	24.6	24.5
Guam	26.0	24.3
Hawaii	26.7	23.5
Idaho	21.7	24.6
Illinois	27.8	22.5
Indiana	20.5	20.6
Iowa	22.6	18.5
Kansas	26.5	18.6
Kentucky	18.7	21.1
Louisiana	18.9	16.9
Maine	24.5	28.0
Maryland	32.8	27.6
Massachusetts	35.4	26.2
Michigan	22.8	22.6
Minnesota	28.8	21.9
Mississippi	17.5	16.8
Missouri	23.0	19.9
Montana	25.1	25.7
Nebraska	25.2	20.9
Nevada	19.9	23.7
New Hampshire	30.2	27.9
New Jersey	32.3	26.4
New Mexico	22.7	23.2
New York	29.9	26.8
North Carolina	23.8	20.6
North Dakota	23.6	22.5
Ohio	22.3	21.0
Oklahoma	20.4	14.6
Oregon	26.1	26.3
Pennsylvania	24.5	24.1
Puerto Rico	19.4	17.7
Rhode Island	27.5	26.1
South Carolina	21.8	17.4
South Dakota	22.9	15.7
Tennessee	20.9	23.3
Texas	23.1	23.8
Utah	25.4	23.3
Vermont	30.2	29.3
Virginia	30.9	27.3
Washington	28.1	28.6
West Virginia	16.1	25.1
Wisconsin	23.6	16.2
Wyoming	21.2	22.7

Graph: To draw the scatterplot of the provided data do the following steps in Minitab mentioned below:

Step 1: Enter the data into Minitab worksheet.

Step 2: Go to Graph, select Scatterplot and select simple and click OK.

Step 3: Select the data variable column of “FruitVeg5” for x-axis and column of “EdCollege” for y-axis click on OK.

The obtained scatterplot is as follows:

Interpretation: The obtained scatterplot of the data is plotted and it shows that there is moderate, linear, and positive relationship between the variables “FruitVeg5” and “EdCollege”.

(b)

To determine

To graph: A regression line to the scatter plot of the data with 5 fruits and vegetables per day and EdCollege.

Explanation of Solution

Graph: To draw the regression line of the provided data do the following steps in Minitab mentioned below:

Step 1: Enter the data into Minitab worksheet.

Step 2: Go to Graph, select Scatterplot and select with regression and click OK.

Step 3: Select the data variable column of “FruitVeg5” for x-axis and column of “EdCollege” for y-axis click on OK.

The obtained scatterplot is as follows:

Interpretation: The obtained scatterplot of the data is plotted with regression line and it is observed that the regression line that fits best to the plot is given by $\text{EdCollege}=4.033+0.9063\left(\text{FruitVeg5}\right)$. Also, the regression line indicates that the relationship between the variables “FruitVeg5” and “EdCollege” is linear and positive.

(c)

To determine

The position of some states in the scatterplot graph and write a summary on the comparison of these states with other states.

Answer to Problem 171E

Solution: The states District of Colombia, Massachusetts and West Virginia are away from the regression line whereas the states like Vermont, Rhode Island, Guam and Louisiana lies on the regression line.

Explanation of Solution

The scatterplot and the regression line of the data of the variables “FruitVeg5” and “EdCollege” is as follows:

From the graph it can be seen that there is an outlier at the upper right of the scatterplot corresponds to District of Colombia, another outlier at the upper right of the scatterplot corresponds to Massachusetts, outlier at the lower middle of the scatterplot corresponds to West Virginia. These states are away from the regression line whereas the states like Vermont, Rhode Island, Guam and Louisiana lies on the regression line.

(d)

To determine

Whether earning a college degree is a cause people eat five servings of fruits and vegetables per day.

Answer to Problem 171E

Solution: The relationship between the variable cannot be considered as a result of the causation because there is a possibility of the presence of lurking and confounding variable.

Explanation of Solution

The scatterplot and the regression line of the data of the variables “FruitVeg5” and “EdCollege” is shown below and it shows that the relationship between the variables is linear and positive.

Though the diagram shows a positive and linear relationship, but it not indicates the causation. It may be possible that the correlation between the variable occurs due to the presence of lurking and confounding variable.