(a)
Construct a
(a)
Answer to Problem 12P
The scatter diagram for data is,
Explanation of Solution
Calculation:
The variable x denotes the age of a licensed driver in years and y denotes the percentage of all fatal accidents due to failure to yield the right-of-way.
Step by step procedure to obtain scatter plot using MINITAB software is given below:
- Choose Graph > Scatterplot.
- Choose Simple. Click OK.
- In Y variables, enter the column of x.
- In X variables, enter the column of y.
- Click OK.
(b)
Verify the values of
(b)
Explanation of Solution
Calculation:
The formula for
In the formula, n is the sample size.
The values are verified in the table below,
x | y | xy | ||
37 | 5 | 1369 | 25 | 185 |
47 | 8 | 2209 | 64 | 376 |
57 | 10 | 3249 | 100 | 570 |
67 | 16 | 4489 | 256 | 1072 |
77 | 30 | 5929 | 900 | 2310 |
87 | 43 | 7569 | 1849 | 3741 |
Hence, the values are verified.
The number of data pairs are
The value of r is 0.943 this shows that r is not –0.943.
Hence, the value of r is verified as approximately 0.943.
(c)
Find the value of
Find the value of
Find the value of a.
Find the value of b.
Find the equation of the least-squares line.
(c)
Answer to Problem 12P
The value of
The value of
The value of a is –27.768.
The value of b is 0.749.
The equation of the least-squares line is
Explanation of Solution
Calculation:
From part (b), the values are
The value of
Hence, the value of
The value of
Hence, the value of
The value of b is,
Hence, the value of b is 0.749.
The value of a is,
Hence, the value of a is –27.768.
The equation of the least-squares line is,
Hence, the equation of the least-squares line is
(d)
Construct a scatter diagram with least squares line.
Locate the point
(d)
Answer to Problem 12P
The scatter diagram with least squares line with point
Explanation of Solution
Calculation:
In the dataset of failure of yield, also include the point
Step by step procedure to obtain scatter plot using MINITAB software is given below:
- Choose Graph > Scatterplot.
- Choose With regression. Click OK.
- In Y variables, enter the column of x.
- In X variables, enter the column of y.
- Click OK.
(e)
Calculate the value of the coefficient of determination
Mention percentage of the variation in y that can be explained by variation in x.
Mention percentage of the variation in y that cannot be explained by variation in x.
(e)
Answer to Problem 12P
The value of the coefficient of determination
The percentage of the variation in y that can be explained by variation in x is 88.9%.
The percentage of the variation in y that cannot be explained by variation in x is 11.1%.
Explanation of Solution
Calculation:
Coefficient of determination
The coefficient of determination
From part (b), the value of
Hence, the value of the coefficient of determination
About 88.9% of the variation in y (percentage of all fatal accidents due to failure to yield the right-of-way) is explained by x (age of a licensed driver in years). Since the value of
Hence, the percentage of the variation in y that can be explained by variation in x is 92%.
About 11.1%
Hence, the percentage of the variation in y that cannot be explained by variation in x is 11.1%.
(f)
Find the percentage of all fatal accidents due to failing to yield the right-of-way for 70-year-olds.
(f)
Answer to Problem 12P
The percentage of all fatal accidents due to failing to yield the right-of-way for 70-year-olds is 24.662%.
Explanation of Solution
Calculation:
From part (c), the equation of the least-squares line is
Substitute
Hence, the percentage of all fatal accidents due to failing to yield the right-of-way for 70-year-olds is 24.662%.
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Chapter 9 Solutions
Understandable Statistics: Concepts and Methods
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