Problem 25 BSC

Regression and Predictions. Exercises use the same data sets as Exercises in Section 10-2. In each case, find the regression equation, letting the first variable be the predictor (x) variable. Find the indicated predicted value by following the prediction procedure summarized in Figure.

Figure

Gas Prices One gas station not included in the table below had a listed price of $2.78 for regular gas. Find the best predicted price of premium gas at this station. Is the result close to the actual price of $2.93 for premium gas?

Regular |
2.77 |
2.77 |
2.79 |
2.81 |
2.78 |
2.86 |
2.75 |
2.77 |

Mid-Grade |
3.00 |
2.77 |
2.89 |
2.93 |
2.93 |
2.96 |
2.86 |
2.91 |

Premium |
3.07 |
3.09 |
3.00 |
3.06 |
3.03 |
3.06 |
3.02 |
3.03 |

Answer :

Step 1 of 1 :

Given

Figure

Gas Prices One gas station not included in the table below had a listed price of $2.78 for regular gas.

Given data

x | y |

2.77 | 3.07 |

2.77 | 3.09 |

2.79 | 3 |

2.81 | 3.06 |

2.78 | 3.03 |

2.86 | 3.06 |

2.75 | 3.02 |

2.77 | 3.03 |

Now we have to determine the equation of the regression line.

The table is given below.

x | y | xy | |

2.77 | 3.07 | 8.5039 | 7.6729 |

2.77 | 3.09 | 8.5593 | 7.6729 |

2.79 | 3 | 8.37 | 7.7841 |

2.81 | 3.06 | 8.5986 | 7.8961 |

2.78 | 3.03 | 8.4234 | 7.7284 |

2.86 | 3.06 | 8.7516 | 8.1796 |

2.75 | 3.02 | 8.305 | 7.5625 |

2.77 | 3.03 | 8.3931 | 7.6729 |

The formula of the the regression line.

= a + bx

where is the dependent variable (that’s the variable that goes on the Y axis).

x is the independent variable (i.e. it is plotted on the X axis).

b is the slope of the line and a is the y-intercept.

Where

a = and

b =

The...