Chapter A, Problem 1P

(a)

To determine

Plot the data and the regression line on the same axes. Does the line fit the data well?

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

$G=3.543+0.734t.$

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 $R^2=\mathrm{0.9729.}$

(b)

To determine

Interpret the slope of the line in terms of gross world product.

Explanation of Solution

The gross world product, G, which measures global output of goods and services is given by

$G\left(t\right)=3.543+0.734t$

Hence, the slope of G ( t ) indicates that gross world product increases by 0.734 trillion dollars every year.

(c)

To determine

Use the regression line to estimate gross world product in 2005 and in 2020. Comment on your confidence in the two predictions.

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

$G=3.543+0.734t.$

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

$G=3.543+0.734t$

$G\left(2005\right)=3.543+0.734\left(2005\right)=1475.213\text{ trillion dollars}$

$G\left(2020\right)=3.543+0.734\left(2020\right)=1486.223\text{ trillion dollars}$

Both predictions cannot be made confidently because:

1. Uniform increase in gross world product every year is highly unlikely in actual scenario.
2. 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.