Question

The following table shows the annual income, in dollars, and amount spent on vacation, in dollars, for a sample of 8 families.

Answer 1

Answer:

a. Scatterplot is attached.

b. Positive Correlation

c. Correlation coefficient=0.9219

Step-by-step explanation:

a.

The following procedure will be used to obtain the scatter plot

•    Open an Google Sheets file online or excel sheet on your computer.
•    In column B and C, enter  the Income and Vacation data  as provided above.
•    Select the data > click on insert CHART.
•    Chose Scatter Chart option

•    Click OK.

A scatter plot visualizing your data should be displayed as attached.

b.

• On your computer, open a spreadsheet in Google Sheets.
• Double-click on your scatter plot.
• At the right, click on Customize  tab and then Series.
• Scroll down and check the Trend line box

-From the trend line, your notice that your variables have a positive correlation.

-As the income increases, so does vacation expenditure.

c. The correlation coefficient can be calculated as follows.

• Click on any empty cell in the sheet and enter the formula
• "=CORREL((y-axis range),(x-axis range))"
• ENTER

-From our Google Sheets calculation our variables have a positive correlation and the correlation coefficient is 0.9219

-The correlation coefficient,r can also be calculated manually:

-let x be income, and y be vacation and divide all the values by 100 to make the smaller and easier to manipulate:

$r=\frac{n(\sum xy)-(\sum x)(\sum y)}{\sqrt{[n\sum x^2-(\sum x)^2][n\sum y^2-(\sum y)^2}}\\\\\\\sum xy=153914\\\sum x=4485\\\sum y=246\\\sum x^2=2878447\\(\sum x)^2=4485^2=20115225\\(\sum y)^2=246^2=60516\\\sum y^2=8392\\n=8\\\\\#substitute \ and \ solve \ for \ r\\\\=\frac{8\times153914-4485\times 246}{\sqrt{[8\times 2878447-4485^2][8\times 8392-246^2]}}\\\\=0.92186\\\\\approx 0.9219$