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A sample of 15, 10 years -old children was taken to study whether watching television reduces the amount of physical exercise, causing weight gains

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A sample of 15, 10 years -old children was taken to study whether watching television reduces the amount of physical exercise, causing weight gains. The number of kilograms each child was overweight by was recorded (a negative number indicates the child is underweight). In addition, the number of hours of television viewing per week was also recorded. These data are listed in the table below.

Television(hours) 42 34 25 35 37 38 31 33 19 29 38 28 29 36 18
Overweight (Kg) 8 3 0 0 6 6 3 3 -4 4 4 2 1 6 -3
  1. Use an appropriate plot to investigate the relationship between Television(hours) and Overweight

(KG). Briefly explain the selection of each variable on the X and Y axes and why? (3 marks)

  1. Calculate and interpret the coefficient of correlation (r) between

Television(hours) and Overweight (KG)(2 marks)

  1. Estimate a simple linear regression model and present the estimated linear equation. Then, interpret the coefficient estimates of the linear model. (3 marks)
  2. Determine the coefficient of determination (R2) and interpret it. (2 marks)
  3. Test the significance of the relationship at the 5% significance level. (3 marks)
  4. What is the value of the standard error of the estimate (se). Then, comment on the fitness of the

linear regression model? (2 marks)
Note: (Answer for question (b) to (f) should be supported with the excel output. Hence, you are required to provide the excel output as the supplementary file(s) in Appendix Section.
Marking criteria

Marking criteria Weighting
Question 4
  1. Choosing dependent and independent variable correctly and presenting the relationship
  2. Calculating correlation and interpreting the value
  3. Estimating regression equation and interpreting slope and intercept coefficient
  4. Estimating coefficient of determination and interpreting values.
15 marks
3 marks
  1. marks
  2. marks

2 marks
  1. Testing the significance of the relationship between Dependent and independent variable of the model.
  2. Calculating standard error of the model and commenting on fitness of the regression model.
3 marks
2 marks
 

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