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 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). Estimate a simple linear regression model and present the estimated linear equation. Then, interpret the coefficient estimates of the linear model. Determine the coefficient of determination (R 2 ) and interpret it.
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
- 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 |
- 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). - Estimate a simple linear regression model and present the estimated linear equation. Then, interpret the coefficient estimates of the linear model.
- Determine the coefficient of determination (R 2 ) and interpret it.
- Test the significance of the relationship at the 5% significance level.
- 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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