Question

Given are five observations collected in a regression study on two variables.

x i |
2 |
6 |
9 |
13 |
20 |

y i |
7 |
18 |
9 |
26 |
23 |

1. Compute SSE, SST, and SSR (round to one decimals).

2. Compute the coefficient of determination (round to four decimals).

3. Compute the mean square error (round to two decimals).

4. Compute the estimated standard deviation of
*b _{1}* (round to four decimals).

5. Compute the *p-value* and t value (test statistic) of
the *t* test to test the following hypotheses (round to
three decimals)

*H _{0}*: β 1 = 0 and

6. Compute the p-value and F value (test statistic) of the F test to test the following hypotheses (round to two decimals):

*H _{0}*: β 1 = 0 and

Answer #1

1)

SSE =Syy-(Sxy)2/Sxx= | 127.3 |

SST=Syy= | 281.2 |

SSR =(Sxy)2/Sxx = | 153.9 |

2)

Coeffficient of determination R^2 =SSR/SST= | 0.5473 |

3)

MSE = | s2 =SSE/(n-2)= | 42.43 |

4)

estimated std error of slope =se(β1) =s/√Sxx= | 0.4726 |

5)

test stat t = | (bo-β1)/se(β1)= | = | 1.904 |

p value: | = | 0.1530 |

6)

Source | SS | df | MS | F | p value |

regression | 153.900 | 1 | 153.900 | 3.627 | 0.153 |

Residual error | 127.300 | 3 | 42.433 | ||

Total | 281.200 | 4 |

test statistic F =3.63

p value =0.1530

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1
2
3
4
5
yi
53
58
47
21
11
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x y
2 12
3 9
6 8
7 7
8 6
7 5
9 2
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