
Concept explainers
(a)
To find: The predicted count values.
(a)

Answer to Problem 74E
Solution: The predicted count values obtained are
Explanation of Solution
Calculation: The provided least-squares regression equation is
The time values are provided in the data as 1, 3, 5, and 7.
Substituting the values of time in the above linear regression equation, the following results are obtained:
For
For
For
For
Hence, the predicted count values obtained are
(b)
Section 1
To find: The difference between the observed and the predicted counts.
(b)
Section 1

Answer to Problem 74E
Solution: The differences obtained are
Explanation of Solution
Calculation: The observed counts are provided in the exercise as
The predicted counts obtained from part (a) are
All of the above values are for the times 1, 3, 5, and 7.
The differences
For
For
For
For
Hence, the differences obtained are
Section 2
The number of positive differences between the observed and the predicted counts.
Section 2

Answer to Problem 74E
Solution: There are three difference values that are positive as
Explanation of Solution
Clearly, the positive difference values are
Hence, three differences
The number of negative differences between the observed and the predicted counts.

Answer to Problem 74E
Solution: The negative difference is
Explanation of Solution
Clearly, the negative difference value is
(c)
Section 1
To find: The squares of the differences obtained in part (b).
(c)
Section 1

Answer to Problem 74E
Solution: The squares of the differences are
Explanation of Solution
Calculation: The differences obtained in the part (b) above are
The squares of the differences obtained are calculated as follows:
The square of the difference
The square of the difference
The square of the difference
The square of the difference
Hence, the squares of the differences obtained are
Section 2
To find: The sum of the squares of the differences obtained in Section 1 above.
Section 2

Answer to Problem 74E
Solution: The sum of the squares of the differences obtained is
Explanation of Solution
Calculation: The squares of the differences are obtained in Section 1 above as
The sum of the differences
Hence, the sum of the differences obtained is
(d)
Section 1
To find: The predicted count values for the new regression equation.
(d)
Section 1

Answer to Problem 74E
Solution: The predicted count values obtained are:
Explanation of Solution
Calculation: The provided least-squares regression equation is
The time values are provided in the data as 1, 3, 5, and 7.
Substituting the values of time in the above linear regression equation, the following results are obtained:
For
For
For
For
Hence, the predicted count values obtained are
Section 2:
To find: The difference between the observed and the predicted counts.
Section 2:

Answer to Problem 74E
Solution: The differences obtained are
Explanation of Solution
Calculation: The observed counts are provided in the exercise as:
The predicted counts obtained from section 1 above are:
In both the cases, the time is 1, 3, 5 and 7 respectively.
The differences
For
For
For
For
Hence, the differences obtained are
Section 3
To find: The number of positive differences between the observed and the predicted counts.
Section 3

Answer to Problem 74E
Solution: None of the differences are positive.
Explanation of Solution
Clearly, none of the difference values are positive. Hence, zero difference values are positive.
To find: The number of negative differences between the observed and the predicted counts.

Answer to Problem 74E
Solution: There are four negative differences as:
Explanation of Solution
Clearly, all of the values are negative. Hence, the differences
Section 4
To find: The squares of the differences obtained in section 2 of part (d).
Section 4

Answer to Problem 74E
Solution: The squares of the differences are
Explanation of Solution
Calculation: The differences obtained in the Section 2 of part (d) above are
The squares of the differences obtained are calculated as follows:
The square of the difference
The square of the difference
The square of the difference
The square of the difference
Hence, the squares of the differences obtained are
Section 5
To find: The sum of the squares of the differences obtained in Section 3 above.
Section 5

Answer to Problem 74E
Solution: The sum of the differences is
Explanation of Solution
Calculation: The squares of the differences are obtained in Section 4 above as
The sum of the differences
Hence, the sum of the differences is
(e)
To explain: The least-squares inference based on the calculations performed.
(e)

Answer to Problem 74E
Solution: The following least-squares regression is a better measure of the relationship between the log count and the time.
Explanation of Solution
The differences (residuals) are both positive and negative values whereas for the regression line
all the differences (residuals) are extremely low negative values. Thus, the residual plots for the first regression line will lie both below and above the x-axis. Also, its predicted regression line will lie much near to the observed regression line. Whereas, the residual plots for the second regression line will lie only below the x-axis, indicating it to be not a much accurate measure. Also, with such low negative differences, the predicted regression line will lie far from the observed regression line. Hence, the first line better predicts the relationship between the variables log count and the time because it gives a better approximate value of the response variable.
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Chapter 2 Solutions
Introduction to the Practice of Statistics
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