   Chapter 4, Problem 12CR Understanding Basic Statistics

8th Edition
Charles Henry Brase + 1 other
ISBN: 9781337558075

Solutions

Chapter
Section Understanding Basic Statistics

8th Edition
Charles Henry Brase + 1 other
ISBN: 9781337558075
Textbook Problem

In Problems 9-14,(a) Draw a scatter diagram for the data.(b) Find x ¯ , y ¯ , b , and the equations of the least-squares line. Plot the line on the scatter diagram of part (a).(c) Find the sample correlation coefficient r and the coefficient of determination r 2 . What percentage of variation in y is explained by the least-squares model?Sales: Insurance Dorothy Kelly sells life insurance for the Prudence Insurance Company. She sells insurance by making visits to her clients' homes. Dorothy believes that the number of sales should depend, to some degree, on the number of visits made. For the past several years, she has kept careful records of the number of visits (x) she makes each week and the number of people (y) who buy insurance that week. For a random sample of 15 such weeks, the x and y values follow: X 11 19 16 13 28 5 20 14 22 7 15 29 8 25 16 y 3 11 8 5 8 2 5 6 8 3 5 10 6 10 7 Complete parts (a) through (c). given ∑ x   =   248 ; ∑ y = 97 ;   ∑ x 2 =   4856 ;       ∑ y 2 = 731 ; ∑ x y =   1825. (d) In a week during which Dorothy makes 18 visits, how many people do you predict will buy insurance from her?

(a)

To determine

To graph: The scatter diagram.

Explanation

Given: The data which consists of variables, ‘number of visits in a week’ and ‘number of people who buy insurance that week’, represented by x and y, respectively, is provided.

Graph:

Follow the steps given below in Excel to obtain the scatter diagram of the data.

Step 1: Enter the data into Excel sheet. The screenshot is given below.

Step 2: Select the data and click on ‘Insert’. Go to charts and select the chart type ‘Scatter’.

(b)

To determine

To find: The values of x¯,y¯, and b, and the equation for the least-squares line.

(c)

To determine

The values of r and r2, and the percentage of variation in y that can be explained by the least-squares model.

(d)

To determine

To find: The least-squares line forecast for y at x=18.

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