Concept explainers
(a)
To explain is a line an appropriate model to use for these data.
(a)
Answer to Problem 59E
Yes, a line appears to be appropriate for these data.
Explanation of Solution
The relationship of the number of Mentos and the amount of coke expelled is given in the question. The
(b)
To find the
(b)
Answer to Problem 59E
Explanation of Solution
The relationship of the number of Mentos and the amount of coke expelled is given in the question. The scatterplot and the residual plot for the same is given. Thus, the coefficient of determination
Thus, the
(c)
To find out what is the equation of least square regression line.
(c)
Answer to Problem 59E
Explanation of Solution
The relationship of the number of Mentos and the amount of coke expelled is given in the question. The scatterplot and the residual plot for the same is given. The general equation of the least square regression line is:
Thus, the estimate of the constant
And the estimate of the slope
Thus, putting the values in the general equation we will get,
(d)
To interpret the value of s and
(d)
Explanation of Solution
The relationship of the number of Mentos and the amount of coke expelled is given in the question. The scatterplot and the residual plot for the same is given. Thus, the standard error of the estimate s is given after “S=” in the computer output as:
As we know that the standard error of the estimate s represents the average error of predictions thus the average deviation between actual and the predicted values. Thus the predicted amount expelled using the equation of least square regression line deviated on average by
Now, the coefficient of determination is given after “R-Sq” in the computer output as:
As we know that the coefficient of determination measures the proportion of variation in the responses y variable that is explained by the least square regression model using the explanatory x variable. Thus, we can say that
Chapter 3 Solutions
PRACTICE OF STATISTICS F/AP EXAM
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