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 a. 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? b. Calculate and interpret the coefficient of correlation (r) between Television(hours) and Overweight (KG). c. Estimate a simple linear regression model and present the estimated linear equation. Then, interpret the coefficient estimates of the linear model. d. Determine the coefficient of determination (R 2 ) and interpret it. e. Test the significance of the relationship at the 5% significance level. f. What is the value of the standard error of the estimate (se). Then, comment on the fitness of the linear regression model?
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
a. 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?
b. Calculate and interpret the coefficient of
c. Estimate a simple linear regression model and present the estimated linear equation. Then, interpret the coefficient estimates of the linear model.
d. Determine the coefficient of determination (R 2 ) and interpret it.
e. Test the significance of the relationship at the 5% significance level.
f. What is the value of the standard error of the estimate (se). Then, comment on the fitness of the linear regression model?
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