Maths – squares equation problem

1. It is generally known that there is a relationship between height (cm) and weight (kg). Data from a particular study on Irish women to quantify this relationship are given below.

Height Weight
1.24 63.96 
1.35 66.33 
1.11 62.91 
1.84 78.57
2.03 80.49 
2.12 81.72 
1.98 78.88 
1.65 73.77
1 58.68
1.5 68.32 
1.79 75.16
1.56 68.5

(a) Estimate the least squares equation.

(b) Measure the strength of the linear relationship between height and weight.

(c) Conduct a Model Utility test on the model. What can you conclude from this test? 

(d) Calculate a 90% confidence interval for the slope of the estimated linear model.

2. A research group are conducting an experiment to study the relationship between fitness levels and the number of hours spent exercising each week. Subjects are randomly selected and, after several fitness tests, are assigned a fitness score. The number of hours spent exercising per week is also recorded. Data for sixteen subjects are given below.

Hours Score
3.2 9.63 
2.5 9.79 
1.7 8.19
2.4 8.57
1.9 7.77 
2.8 11.33
3 11.32 
4.2 12.66 
1.1 7.63
0.5 6.85 
0.7 4.42
1.6 4.92 
2.9 11.6
3.7 13.94
1.4 6.12

(a) Fit a simple linear regression model to the following data (taking Score as the de- pendent variable).
(b) Interpret the regression parameters in the given situation.
(c) Conduct a Model Utility test on the model. What can you conclude from this test?
(d) What proportion of the total sample variability in fitness scores is explained by hours spent exercising?
(e) Calculate a 90% confidence interval for the slope of the estimated linear model.

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