A sample of 19 school children was randomly selected and their age, height and weight was recorded for each child. The results are given below. The goal is to predict the weight of the child by using the height and age.

Name |
Height |
Weight |
Age |

Alfred |
69.0 |
112.5 |
14 |

Alice |
56.5 |
84 |
13 |

Barbara |
65.3 |
98 |
13 |

Carol |
62.8 |
102.5 |
14 |

Henry |
63.5 |
102.5 |
14 |

James |
57.3 |
83 |
12 |

Jane |
59.8 |
84.5 |
12 |

Janet |
62.5 |
112.5 |
15 |

Jeffrey |
62.5 |
84 |
13 |

John |
59.0 |
99.5 |
12 |

Joyce |
51.3 |
50.5 |
11 |

Judy |
64.3 |
90 |
14 |

Louise |
56.3 |
77 |
12 |

Mary |
66.5 |
112 |
15 |

Philip |
72.0 |
150 |
16 |

Robert |
64.8 |
128 |
12 |

Ronald |
67.0 |
133 |
15 |

Thomas |
57.5 |
85 |
11 |

William |
66.5 |
112 |
15 |

*a*) Perform a simple linear regression using weight as the response variable and height as the predictor variable. Be sure to address the following:

* i*) What is the least squares line?

* ii*) Is height useful (use α = 0.05) in predicting weight?

* iii*) What proportion of the total variation in the weight can be explained by the height?

* iv*) Include a plot of weight v height with the regression line. How does it look?

*v*) Check that the regression assumptions are satisfied.

*vi*) What would you predict the weight to be of a school child whose height is 59? Give a 95% prediction interval for this estimate.

*b*) Perform a simple linear regression using weight as the response variable and age as the predictor variable. Be sure to address the following:

* i*) What is the least squares line?

* ii*) Is age useful (use α = 0.05) in predicting weight?

* iii*) What proportion of the total variation in the weight can be explained by the age?

* iv*) Include a plot of weight v age with the regression line. How does it look?

*v*) Check that the regression assumptions are satisfied.

*vi*) What would you predict the weight to be of a 13 year old school child? Give a 95% prediction interval for this estimate.

*c*) Fit a first order multiple regression model, using weight as the response variable and height and age as predictor variables. Be sure to address the following:

* i*) What are the least squares estimates?

* ii*) What proportion of the total variation in the weight can be explained by this model? How about after adjusting for the number of terms in the model.

* iii*) Is height useful (use α = 0.05) in predicting weight, when age is taken into consideration?

* iv*) Is age useful (use α = 0.05) in predicting weight, when height is taken into consideration?

*d*) Summarize your results.

*i*) Which of the three models would you use? Explain why.

*ii*) Predict the weight of a 13 year-old school child with a height of 59, with a prediction interval.

*iii*) Would it be appropriate to use this model to predict weights for adults? Explain why or why not.

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