(a)
Construct a
(a)
Answer to Problem 9P
The scatter diagram for data is,
Explanation of Solution
Calculation:
The variable x denotes the weight of the car (in hundreds of pounds) and y denotes the miles per gallon (mpg).
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 | ||
27 | 30 | 729 | 900 | 810 |
44 | 19 | 1936 | 361 | 836 |
32 | 24 | 1024 | 576 | 768 |
47 | 13 | 2209 | 169 | 611 |
23 | 29 | 529 | 841 | 667 |
40 | 17 | 1600 | 289 | 680 |
34 | 21 | 1156 | 441 | 714 |
52 | 14 | 2704 | 196 | 728 |
Hence, the values are verified.
The number of data pairs are
Hence, the value of r is verified as approximately –0.946.
(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 9P
The value of
The value of
The value of a is 43.326.
The value of b is –0.6007.
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 –0.6007.
The value of a is,
Hence, the value of a is 43.326.
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 9P
The scatter diagram with least squares line with point
Explanation of Solution
Calculation:
In the dataset of eight weights and miles per gallon 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)
Find 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 9P
The value of the coefficient of determination
The percentage of the variation in y that can be explained by variation in x is 89.4%.
The percentage of the variation in y that cannot be explained by variation in x is 10.6%.
Explanation of Solution
Calculation:
Coefficient of determination
The coefficient of determination
From part (b), the value of correlation coefficient r is –0.946. The value of
Hence, the value of the coefficient of determination
About 89.4% of the variation in y (miles per gallon (mpg)) is explained by x (weight of the car (in hundreds of pounds)). Since the value of
Hence, the percentage of the variation in y that can be explained by variation in x is 89.4%.
About 10.6%
Hence, the percentage of the variation in y that cannot be explained by variation in x is 10.6%.
(f)
Find the number of miles per gallon for car weight
(f)
Answer to Problem 9P
The number of miles per gallon for car weight
Explanation of Solution
Calculation:
From part (c), the equation of the least-squares line is
Substitute
Hence, the number of miles per gallon for car weight
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Chapter 9 Solutions
Understandable Statistics: Concepts and Methods
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