Chapter 14.4, Problem 35E

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11th Edition

Ronald J. Harshbarger + 1 other

ISBN: 9781305108042

Textbook Problem

** World population** The table gives the actual or projected world population in billions for selected years from 2000 to 2050.

(a) Use linear regression to find the linear equation that is the best fit for the data, with *x* equal to the number of years past 2000.

(b) Use the equation to predict the population in 2018.

(c) Write a sentence that interprets the slope of the linear regression line.

Years |
Population (billions) |

2000 | 6.08 |

2010 | 6.82 |

2020 | 7.54 |

2030 | 8.18 |

2040 | 8.72 |

2050 | 9.19 |

*Source:* U.S. Bureau of the Census, International Data Base

**(a)**

To determine

**To calculate:** The linear equation of the line that is the best fit for the data using linear regression, with *x* equal to the number of years past 2000. Report the model with 3 significant digits. The world population in billion is tabulated below for their respective years.

Years | Population (in billions) |

Explanation

**Given Information:**

The world population in billion is tabulated below for their respective years.

Years | Population (in billions) |

**Formula used:**

The equation of the best fit line by linear regression that for the given data points

Where

**Calculation:**

Consider the table,

Years | Population (in billions) |

Let

That is,

Let

That is,

Since, the number of data points is

The value of *b* for a best fit line from a linear regression is,

Substitute 6 for *n* in

**(b)**

To determine

**To calculate:** The population in 2025. The world population in billion is tabulated below for their respective years.

Years | Population (in billions) |

**(c)**

To determine

The interpretation of the slope of the best fit line. The table gives the actual or projected world population in billions for selected years from 2000 to 2050.

Years | Population (in billions) |

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