Concept explainers
(a)
To find: The slope of the line
(a)
Answer to Problem 40E
The slope is b = -19.87
Explanation of Solution
Given:
The equation of the least squares line is
Calculation:
On comparing our equation to general equation of regression we get, the slope is: b = -19.87
This tells us that the gas consumed is predicted to go down by -19.87cubic feet for each added temperature.
Conclusion:
Hence, the slope is: b = -19.87.
(b)
To identify: the y intercept of the line and explain why the y intercept is risky to use.
(b)
Answer to Problem 40E
The Y intercept is: a = 1425
Explanation of Solution
Calculation:
On comparing our equation to general equation of regression we get, the Y intercept is:
The Y intercept of a regression line
Conclusion:
Hence, the Y intercept is:
This prediction is of no statistical use unless X can actually take values near 0 that’s why it’s risky to use this value as a prediction.
(c)
To predict: the amount of natural gas Joan will use in a month
(c)
Answer to Problem 40E
Joan uses 828.9 cubic gas.
Explanation of Solution
Calculation:
The regression line is:
At temperature (X) =
This shows that Joan uses 828.9 cubic feet gas (approx.) to maintain the temperature 30 degrees Fahrenheit.
Conclusion:
Hence, Joan uses 828.9 cubic feet gas (approx).
Chapter 3 Solutions
The Practice of Statistics for AP - 4th Edition
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