Mathematics, 15.04.2020 01:19 lexipiper8296

The following table shows the annual income, in dollars, and amount spent on vacation, in dollars, for a sample of 8 families.
Income 41,100 53,000 27,400 34,400 65,800 98,100 72,000 56,700
Vacation 2,700 2,400 1,700 2,500 2,800 5,100 4,200 3,200

(a) Create a scatterplot of the data in the table.

(b) Describe the association shown in the scatterplot created in part (a).

(c) Calculate the coefficient of determination for the data, and interpret the value in context.

Answers: 3

Show answers

Answers

Answer from: alissa64

The scatterplot of the data involves producing a graphical plot of the distribution by denoting each pair of (x, y) points by a dot or mark.

The slope of the regression line slopes towards the positive direction, hence, the relationship between the two variables is positive.

The Coefficient of DETERMINATION, R² which gives the proportion of variation explained by the regression line is 0.85

The table of values :

Income (X) ____ Vacation (Y) 41100 _______ 270053000 ______ 240027400 ______ 170034400 ______ 250065800 ______ 280098100 _______510072000 ______ 420056700 ______ 3200Using a regression calculator or excel, the correlation Coefficient, R between income and vacation is 0.922. The squared value of R, which is R² is the value of the correlation Coefficient ; Hence, R² = 0.922² = 0.85 The slope of regression line is positive, hence the relationship between income and vacation is positive. Also, since the value of the correlation Coefficient, R is positive, the relationship will also be positive.

Learn more :link

The following table shows the annual income, in dollars, and amount spent on vacation, in dollars, f

Answer from: VonneB1684

a. Scatterplot is attached.

b. Positive Correlation

c. Correlation coefficient=0.9219

Step-by-step explanation:

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.

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:

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