Loose-leaf Version for The Basic Practice of Statistics 7e & LaunchPad (Twelve Month Access)
Loose-leaf Version for The Basic Practice of Statistics 7e & LaunchPad (Twelve Month Access)
7th Edition
ISBN: 9781319019334
Author: David S. Moore, William I. Notz, Michael A. Fligner
Publisher: W. H. Freeman
Question
Book Icon
Chapter 7, Problem 7.38TY

a.

To determine

The scatter plot of the given data of smokers and years.

a.

Expert Solution
Check Mark

Answer to Problem 7.38TY

The scatter plot is shown below,

Loose-leaf Version for The Basic Practice of Statistics 7e & LaunchPad (Twelve Month Access), Chapter 7, Problem 7.38TY , additional homework tip  1

Figure (1)

Explanation of Solution

Given Info:

The percentages of adult smokers in the years between 1965 and 2011 is given below,

YearsSmokers
196541.9
197437
197933.3
198331.9
198728.6
199025.3
199324.8
199724.6
200023.1
200222.5
200620.8
200920.6
201119

Software Procedure:

Step by step procedure to draw the scatterplot using the Excel:

Steps to draw a scatter plot of the given data are:

  • Press [Ctrl]-N for a new workbook.
  • Enter the years column A.
  • Enter the percent of adult smokers into column B.
  • Select Add ins then Megastats.
  • Select Correlation/Regression and under that select scatter plot.
  • Select the column 1 in horizontal axis and column 2 in vertical axis.
  • Tick the plot linear regression line and press Ok.

Output using the Excel is given below:

Loose-leaf Version for The Basic Practice of Statistics 7e & LaunchPad (Twelve Month Access), Chapter 7, Problem 7.38TY , additional homework tip  2

Observation:

The scatter plot shows that, the number of smokers’ decreases as the year’s increases.

b.

To determine

The direction, form, and strength of the relationship between percent of smokers and year. Whether there are any outliers.

b.

Expert Solution
Check Mark

Explanation of Solution

From the scatterplot, it is clear that the value of smokers decreases with increase in number of year that means there is a linear relationship between smokers and years and number of smokers decreases with increase in year so, relationship is negative.

Thus, there is a strong negative linear relationship between the smokers and the year and there are no outliers.

c.

To determine

The least squares regression line that predicts percent of smokers from year and add the line to the scatter plot.

c.

Expert Solution
Check Mark

Answer to Problem 7.38TY

The equation of the least square regression line is y^=1003.28+(0.49)x .

Explanation of Solution

Given info:

The given values are,

x¯=1992,y¯=27.2,sx=14,sy=7,r=0.98

Calculation:

The formula for regression equation is given below,

y^=a+bx (1)

Where,

  • b=r×sysx
  • a=y¯bx¯

The formula to calculate the value of b is,

b=r×sysx

Substitute 0.98 for r, 14 for sx and 7 for sy to find the value of b.

b=0.98×714=0.982=0.49

The value of b is 0.49 .

The formula to calculate the value of a is,

a=y¯bx¯

Substitute 27.2 for y¯ , 1992 for x¯ and 0.49 for b to find the value of b.

a=27.2(0.49×1992)=27.2+976.08=1003.28

The value of a is 1003.28 .

Substitute 1003.28 for a and 0.49 for b to find the least square regression line.

y^=1003.28+(0.49)x=1003.280.49x

Thus, the equation of the least square regression line is y^=1003.28+(0.49)x .

d.

To determine

The decline in smoking per year on an average during this period.

d.

Expert Solution
Check Mark

Answer to Problem 7.38TY

The decline in smoking per year on an average during this period is 0.49 .

Explanation of Solution

Calculation:

The equation of the least square regression line is,

y^=1003.280.49x

The slope of the regression is 0.49 .

The coefficient value for year is 0.49 . This coefficient value shows that there is a change in smokers for every unit decreases in additional year.

Thus, the decline in smoking per year on an average during this period is 0.49 .

e.

To determine

The percentage of the variation of adults who smoke can be explained by linear change over time.

e.

Expert Solution
Check Mark

Answer to Problem 7.38TY

The percentage of the variation of adults who smoke can be explained by linear change over time is 96.04%.

Explanation of Solution

Calculation:

The formula to find percentage of the variation of adults who smoke can be explained by linear change over time is given by squared value of r.

r2=(0.98)2=0.9604=96.04%

Thus, the percentage of the variation of adults who smoke can be explained by linear change over time is 96.04%.

f.

To determine

The percentage of smokers in 2020.

f.

Expert Solution
Check Mark

Answer to Problem 7.38TY

The predicted percentage of adults that smoke in 2020 is 13.48%.

Explanation of Solution

Calculation:

From part (c) the equation for linear regression is given by,

y^=1003.28+(0.49)x

Where,

  • x represents the year.
  • y^ represents the percentage of smokers in that particular year.

Substitute 2020 for x in the above equation to find the percentage of smokers in 2020.

y^=1003.28+(0.49)(2020)=1003.28989.8=13.48

Thus, the predicted percentage of adults that smoke in 2020 is 13.48%.

g.

To determine

The percentage of smokers in 2075. And reason that it is foolishness to use this regression line equation to find the percentage of smokers in 2075.

g.

Expert Solution
Check Mark

Answer to Problem 7.38TY

The predicted percentage of adults that smoke in 2075 is 13.48%.

Explanation of Solution

Calculation:

From part (c) the equation for linear regression is given by,

y^=1003.28+(0.49)x

Where,

  • x represents the year.
  • y^ represents the percentage of smokers in that particular year.

Substitute 2075 for x in the above equation to find the percentage of smokers in 2075.

y^=1003.28+(0.49)(2075)=1003.281016.75=13.47

Thus, the predicted percentage of adults that smoke in 2020 is 13.47% .

Clearly, the percentage of smokers came out to be negative in 2075 which is impossible.

Thus, it is foolishness to use this regression line equation to find the percentage of smokers in 2075.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!
Knowledge Booster
Background pattern image
Recommended textbooks for you
Text book image
MATLAB: An Introduction with Applications
Statistics
ISBN:9781119256830
Author:Amos Gilat
Publisher:John Wiley & Sons Inc
Text book image
Probability and Statistics for Engineering and th...
Statistics
ISBN:9781305251809
Author:Jay L. Devore
Publisher:Cengage Learning
Text book image
Statistics for The Behavioral Sciences (MindTap C...
Statistics
ISBN:9781305504912
Author:Frederick J Gravetter, Larry B. Wallnau
Publisher:Cengage Learning
Text book image
Elementary Statistics: Picturing the World (7th E...
Statistics
ISBN:9780134683416
Author:Ron Larson, Betsy Farber
Publisher:PEARSON
Text book image
The Basic Practice of Statistics
Statistics
ISBN:9781319042578
Author:David S. Moore, William I. Notz, Michael A. Fligner
Publisher:W. H. Freeman
Text book image
Introduction to the Practice of Statistics
Statistics
ISBN:9781319013387
Author:David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:W. H. Freeman