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(a)
Plot the data and the regression line on the same axes. Does the line fit the data well?
(a)
Answer to Problem 1P
Yes, the line fits the data well
Explanation of Solution
Given information:
Table gives the gross world product, G, which measures output of goods and services. If t is in years since 1950, the regression line these data is
G in tillions of 1999 dollars.
| Year | 1950 | 1960 | 1970 | 1980 | 1990 | 2000 |
| G | 6.4 | 10.0 | 16.3 | 23.6 | 31.9 | 43.2 |
Calculation:
Yes, the line fits the data well (is in fact the linear regression line) with
(b)
Interpret the slope of the line in terms of gross world product.
(b)
Explanation of Solution
The gross world product, G, which measures global output of goods and services is given by
Hence, the slope of G ( t ) indicates that gross world product increases by 0.734 trillion dollars every year.
(c)
Use the regression line to estimate gross world product in 2005 and in 2020. Comment on your confidence in the two predictions.
(c)
Answer to Problem 1P
The gross world product in 2005 = 1475.213 trillion dollars
The gross world product in 2020 = 1486.223 trillion dollars
Both predictions cannot be made confidently.
Explanation of Solution
Given information:
Table A.5 gives the gross world product, G, which measures output of goods and services. If t is in years since 1950, the regression line these data is
| Year | 1950 | 1960 | 1970 | 1980 | 1990 | 2000 |
| G | 6.4 | 10.0 | 16.3 | 23.6 | 31.9 | 43.2 |
Calculation:
The gross world product, G, which measures global output of goods and services is given by
Both predictions cannot be made confidently because:
- Uniform increase in gross world product every year is highly unlikely in actual scenario.
- A recession (for example the one in 2009) can also lead to decrease in gross world product.
Thus, the gross world product in 2005 = 1475.213 trillion dollars
The gross world product in 2020 = 1486.223 trillion dollars
Both predictions cannot be made confidently.
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Chapter A Solutions
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