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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?

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Understanding Basic Statistics

8th Edition
Charles Henry Brase + 1 other
Publisher: Cengage Learning
ISBN: 9781337558075
BuyFind

Understanding Basic Statistics

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

Solutions

Chapter
Section
Chapter 4, Problem 12CR
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?

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Chapter 4 Solutions

Understanding Basic Statistics
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Ch. 4.1 - Interpretation Trevor conducted a study and found...Ch. 4.1 - Interpretation Do people who spend more time on...Ch. 4.1 - Veterinary Science: Shetland Ponies How much...Ch. 4.1 - Health Insurance:Administrative Cost The following...Ch. 4.1 - Meteorology: Cyclones Can a low barometer reading...Ch. 4.1 - Geology: Earthquakes Is the magnitude of an...Ch. 4.1 - Baseball: Batting Averages and Home Runs In...Ch. 4.1 - University Crime: FBI Report Do larger...Ch. 4.1 - Expand Your Knowledge: Effect of Scale on Scatter...Ch. 4.1 - Expand Your Knowledge: Effect on r of Exchanging x...Ch. 4.1 - Expand Your Knowledge: Using a Table to Test The...Ch. 4.1 - Expand Your Knowledge: Sample Size and...Ch. 4.1 - Expand Your Knowledge: Correlation of Averages...Ch. 4.2 - Statistical Literacy In the least-squares line...Ch. 4.2 - Statistical Literacy In the least squares line...Ch. 4.2 - Critical Thinking When we use a least-squares line...Ch. 4.2 - Critical Thinking If two variables have a negative...Ch. 4.2 - Critical Thinking: Interpreting Computer Printouts...Ch. 4.2 - Critical Thinking: Interpreting Computer Printouts...Ch. 4.2 - Economics: Entry-Level Jobs An economist is...Ch. 4.2 - Ranching: Cattle You are the foreman of the Bar-S...Ch. 4.2 - Weight of Car: Miles per Gallon Do heavier cars...Ch. 4.2 - Basketball: Fouls Data for this problem are based...Ch. 4.2 - Auto Accidents: Age Data for this problem are...Ch. 4.2 - Auto Accidents: Age Let x be the age of a licensed...Ch. 4.2 - Incoine: Medicai Care Let x be per capita income...Ch. 4.2 - Violent Crimes: Prisons Does prison really deter...Ch. 4.2 - Education: Violent Crime The following data are...Ch. 4.2 - Research: Patents The following data are based on...Ch. 4.2 - Archaeology: Artifacts Data for this problem are...Ch. 4.2 - Cricket Chirps: Temperature Anyone who has been...Ch. 4.2 - Expand Your Knowledge: Residual Plot The...Ch. 4.2 - Residual Plot: Miles per Gallon Consider the data...Ch. 4.2 - Expand Your knowledge: Logarithmic...Ch. 4.2 - Expand Your Knowledge: Logarithmic...Ch. 4.2 - Expand Your Knowledge: Logarithmic...Ch. 4.2 - Expand Your Knowledge: Logarithmic...Ch. 4 - Terminology Consider the equation of a...Ch. 4 - Terminology Consider the values of the sample...Ch. 4 - Terminology Suppose we have a set of ordered pairs...Ch. 4 - Terminology Consider the following terms in a...Ch. 4 - Statistical Literacy Suppose the scatter diagram...Ch. 4 - Critical Thinking Suppose you and a friend each...Ch. 4 - Statistical Literacy When using the least-squares...Ch. 4 - StatisticalLiteracy Suppose that for x = 3. the...Ch. 4 - In Problems 9-14, (a) Draw a scatter diagram for...Ch. 4 - In Problems 9-14, (a) Draw a scatter diagram for...Ch. 4 - In Problems 9-14, (a) Draw a scatter diagram for...Ch. 4 - In Problems 9-14, (a) Draw a scatter diagram for...Ch. 4 - In Problems 9-14, (a) Draw a scatter diagram for...Ch. 4 - In Problems 9-14, (a) Draw a scatter diagram for...Ch. 4 - The data in this section are taken from this...Ch. 4 - The data in this section are taken from this...Ch. 4 - The data in this section are taken from this...Ch. 4 - The data in this section are taken from this...Ch. 4 - The data in this section are taken from this...Ch. 4 - The data in this section are taken from this...

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