Use an appropriate plot to investigate the relationship between Television(hours) and Overweight 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 (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) (3 marks) 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. Determine the coefficient of determination (R2) 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?
Correlation
Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.
Linear Correlation
A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related.
Regression Analysis
Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.
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.
- Use an appropriate plot to investigate the relationship between Television(hours) and Overweight
|
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 |
(KG). Briefly explain the selection of each variable on the X and Y axes and why? b. Calculate and interpret the coefficient of
(3 marks)
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.
- Determine the coefficient of determination (R2) 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? (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.
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