Question

You are given the following data set: {(0,0), (0.5,0.6), (1,0.9), (1.1, 1), (1.5, 1.7)}, where the first coordinate is the independent (explanatory) variable, and the second coordinate is the dependent variable.

(a) Find a best fit model if the model is restricted to just be a constant (i.e. the best fit line has slope 0). (b) What is the mean squared error of (a)?

(c) What is the mean squared error of the model that has
y-intercept 0 and slope 1? How much of the variation of the data
can be explained by the independent variable (i.e. what is the
*R*2) using the model from part (c)?

Answer #1

Solution:

X |
Y |

0 |
0 |

0.5 |
0.6 |

1 |
0.9 |

1.1 |
1 |

1.5 | 1.7 |

Go tot data analysis>Regression

SUMMARY OUTPUT | ||||||

Regression Statistics | ||||||

Multiple R | 0.978388 | |||||

R Square | 0.957243 | |||||

Adjusted R Square | 0.94299 | |||||

Standard Error | 0.147766 | |||||

Observations | 5 | |||||

ANOVA | ||||||

df | SS | MS | F | Significance F | ||

Regression | 1 | 1.466496 | 1.466496 | 67.16317 | 0.003802 | |

Residual | 3 | 0.065504 | 0.021835 | |||

Total | 4 | 1.532 | ||||

Coefficients | Standard Error | t Stat | P-value | Lower 95% | Upper 95% | |

Intercept | -0.01528 | 0.123525 | -0.12371 | 0.909364 | -0.40839 | 0.37783 |

X | 1.043027 | 0.127271 | 8.195314 | 0.003802 | 0.637993 | 1.44806 |

Solutionc:

MSE=0.021835

model is

y=-0.01528+1.043027X

R sq=0.9572=0.9572*100=95.72% varaition in dependent varaible is expalined by independent variable good model.

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74.543729
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109.02019
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