Concept explainers
a.
Find the value of r, for which, the value of
Identify the least squares line in this situation.
a.
Answer to Problem 53E
The value of r, for which, the value of
The least squares line in this situation is
Explanation of Solution
Calculation:
It is given that the residual sum of squares can be expressed as
If the value of
Thus, the value of r, for which, the value of
Alternate form of the regression equation:
A regression equation involving one response variable, y and one predictor, x can be expressed as:
Substitute
Thus, the least squares line in this situation is
b.
Find the value of r, for which, the value of
b.
Answer to Problem 53E
The value of r, for which, the value of
Explanation of Solution
Calculation:
If the value of
Thus, the value of r, for which, the value of
c.
Find the value of
c.
Answer to Problem 53E
The value of
Explanation of Solution
Calculation:
For the given institute, the value of r is approximately 0.80; average height at 6 years is 46 inches with standard deviation 1.7 inches; average height at 18 years is 70 inches with standard deviation 2.5 inches.
Consider the given relation
Here,
Thus, the value of
d.
Find the least-squares equation to predict the height at 6 years, using the height at 18 years.
Find the corresponding value of
d.
Answer to Problem 53E
The least-squares equation to predict the height at 6 years, using the height at 18 years is
The corresponding value of
Explanation of Solution
Calculation:
Consider the form of the least-squares equation given in Part a:
Under this consideration,
Thus, the least-squares equation to predict the height at 6 years, using the height at 18 years is
Substitute the above mentioned values in the relation
Thus, the corresponding value of
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Chapter 5 Solutions
Introduction To Statistics And Data Analysis
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