Concept explainers
(a)
>The least squares regression line for the given data set.
(a)
>Answer to Problem 24E
Explanation of Solution
Given information:
The following table represents the ages of the last
U.S. presidents and their wives on the first day of their presidencies:
Concepts Used:
The equation for least-square regression line:
Where
The
Where,
The standard deviations are given by:
Calculation:
The mean of
The mean of
The data can be represented in tabular form as:
Hence, the standard deviation is given by:
And,
Consider,
Putting the values in the formula,
Putting the values to obtain
Putting the values to obtain
Hence, the least-square regression line is given by:
Therefore, the least squares regression line for the given data set is
(b)
>The coefficient of determination.
(b)
>Answer to Problem 24E
Explanation of Solution
Given information:
Same as part
Calculation:
From part
The coefficient of determination is given by:
Where
Putting the values to obtain Coefficient of Determination,
Therefore, the Coefficient of Determination is
(c)
>A
(c)
>Answer to Problem 24E
Explanation of Solution
Given information:
Same as part
Calculation:
Consider age of the president as
The points representing the data would be given by:
Plotting the points to make a scatter plot:
(d)
>The outlier points.
(d)
>Answer to Problem 24E
Explanation of Solution
Given information:
Same as part
Calculation:
From the given table, it can be seen that among all the
Therefore, the outlier point would be
(e)
>The least squares regression line for the given data set by excluding the outlier.
(e)
>Answer to Problem 24E
Explanation of Solution
Given information:
Same as part
Concepts used:
The equation for least-square regression line:
Where
The correlation coefficient of a data is given by:
Where,
The standard deviations are given by:
Calculation:
From part
Excluding the outlier,
The mean of
The mean of
The data can be represented in tabular form as:
Hence, the standard deviation is given by:
And,
Consider,
Putting the values in the formula,
Putting the values to obtain
Putting the values to obtain
Hence, the least-square regression line is given by:
Therefore, the least squares regression line for the given data set by removing the outlier is
(f)
>Whether the outlier is influential.
(f)
>Answer to Problem 24E
The outlier is influential.
Explanation of Solution
Given information:
Same as part
Calculation:
From part
From part
From the equations, it can be seen that removing the outlier creates a great difference in the equation of the least square regression line.
Therefore, the outlier is influential.
(g)
>The coefficient of determination for the data set with the outlier removed.
(g)
>Answer to Problem 24E
Coefficient of Determination is
The proportion of variation is more without the outlier.
Explanation of Solution
Given information:
Same as part
Calculation:
From part
The coefficient of determination is given by:
Where
Plugging the values to obtain Coefficient of Determination,
Therefore, the Coefficient of Determination is
Here the coefficient of determination increased without the outlier.
Hence, the proportion of variance explained is more without the outlier.
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- College AlgebraAlgebraISBN:9781305115545Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage LearningLinear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage LearningGlencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw Hill