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

Question

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Answer 1

Question

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?

(a)

Expert Solution

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:

EBK APPLIED CALCULUS, ENHANCED ETEXT, Chapter A, Problem 1P

Yes, the line fits the data well (is in fact the linear regression line) with R2=0.9729.

(b)

To determine

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

(b)

Expert Solution

Explanation of Solution

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

G(t)=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.

(c)

Expert Solution

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(2005)=3.543+0.734(2005)=1475.213 trillion dollars

G(2020)=3.543+0.734(2020)=1486.223 trillion dollars

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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Answer 2

Question

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?

(a)

Expert Solution

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:

EBK APPLIED CALCULUS, ENHANCED ETEXT, Chapter A, Problem 1P

Yes, the line fits the data well (is in fact the linear regression line) with R2=0.9729.

(b)

To determine

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

(b)

Expert Solution

Explanation of Solution

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

G(t)=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.

(c)

Expert Solution

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(2005)=3.543+0.734(2005)=1475.213 trillion dollars

G(2020)=3.543+0.734(2020)=1486.223 trillion dollars

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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Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Answer 3

Question

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?

(a)

Expert Solution

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:

EBK APPLIED CALCULUS, ENHANCED ETEXT, Chapter A, Problem 1P

Yes, the line fits the data well (is in fact the linear regression line) with R2=0.9729.

(b)

To determine

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

(b)

Expert Solution

Explanation of Solution

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

G(t)=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.

(c)

Expert Solution

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(2005)=3.543+0.734(2005)=1475.213 trillion dollars

G(2020)=3.543+0.734(2020)=1486.223 trillion dollars

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.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Answer 4

Question

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?

(a)

Expert Solution

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:

EBK APPLIED CALCULUS, ENHANCED ETEXT, Chapter A, Problem 1P

Yes, the line fits the data well (is in fact the linear regression line) with R2=0.9729.

(b)

To determine

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

(b)

Expert Solution

Explanation of Solution

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

G(t)=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.

(c)

Expert Solution

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(2005)=3.543+0.734(2005)=1475.213 trillion dollars

G(2020)=3.543+0.734(2020)=1486.223 trillion dollars

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.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Answer 5

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?

(a)

Expert Solution

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:

EBK APPLIED CALCULUS, ENHANCED ETEXT, Chapter A, Problem 1P

Yes, the line fits the data well (is in fact the linear regression line) with R2=0.9729.

(b)

To determine

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

(b)

Expert Solution

Explanation of Solution

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

G(t)=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.

(c)

Expert Solution

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(2005)=3.543+0.734(2005)=1475.213 trillion dollars

G(2020)=3.543+0.734(2020)=1486.223 trillion dollars

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.

Answer 6

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?

(a)

Expert Solution

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:

EBK APPLIED CALCULUS, ENHANCED ETEXT, Chapter A, Problem 1P

Yes, the line fits the data well (is in fact the linear regression line) with R2=0.9729.

Answer 7

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 8

(a)

Expert Solution

Answer to Problem 1P

Yes, the line fits the data well

Answer 9

(a)

Expert Solution

Answer 10

(a)

Expert Solution

Answer 11

Expert Solution

Answer 12

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:

EBK APPLIED CALCULUS, ENHANCED ETEXT, Chapter A, Problem 1P

Yes, the line fits the data well (is in fact the linear regression line) with R2=0.9729.

Answer 13

(b)

To determine

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

(b)

Expert Solution

Explanation of Solution

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

G(t)=3.543+0.734t

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

Answer 14

(b)

To determine

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

Answer 15

(b)

Expert Solution

Explanation of Solution

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

G(t)=3.543+0.734t

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

Answer 16

(b)

Expert Solution

Answer 17

(b)

Expert Solution

Answer 18

Expert Solution

Answer 19

(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.

(c)

Expert Solution

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(2005)=3.543+0.734(2005)=1475.213 trillion dollars

G(2020)=3.543+0.734(2020)=1486.223 trillion dollars

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.

Answer 20

(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 21

(c)

Expert Solution

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.

Answer 22

(c)

Expert Solution

Answer 23

(c)

Expert Solution

Answer 24

Expert Solution

Answer 25

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(2005)=3.543+0.734(2005)=1475.213 trillion dollars

G(2020)=3.543+0.734(2020)=1486.223 trillion dollars

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.