# 1

A company wants to predict the annual value of its total sales based on the national income of the country where is does business. The relationship is represented in the following table:

X | 189 | 190 | 208 | 227 | 239 | 252 | 257 | 274 | 293 | 308 | 316 |

Y | 402 | 404 | 412 | 425 | 429 | 436 | 440 | 447 | 458 | 469 | 469 |

**x** represents the national income in millions of dollars and **y** represents the company's sales in thousands of dollars in the period from 1990 to 2000 (inclusive). Calculate:

1 The regression line of y on x.

2 The linear correlation coefficient and interpret it.

3 If in 2001, the country's national income was 325 million dollars, what would the prediction for the company's sales be?

x_{i} |
y_{i} |
x_{i} ·y_{i} |
x_{i}^{2} |
y_{i2 } |
---|---|---|---|---|

189 | 402 | 35,721 | 161,604 | 75,978 |

190 | 404 | 36,100 | 163,216 | 76,760 |

208 | 412 | 43,264 | 169,744 | 85,696 |

227 | 425 | 51,529 | 180,625 | 96,475 |

239 | 429 | 57,121 | 184,041 | 102,531 |

252 | 436 | 63,504 | 190,096 | 109,872 |

257 | 440 | 66,049 | 193,600 | 113,080 |

274 | 447 | 75,076 | 199,809 | 122,478 |

293 | 458 | 85,849 | 209,764 | 134,194 |

308 | 469 | 94,864 | 219,961 | 144,452 |

316 | 469 | 99,856 | 219,961 | 148,204 |

2,753 | 4,791 | 708,933 | 2,092,421 | 1,209,720 |