2022-09-03

(a) Give examples of two variables that have a strong positive linear correlation and two variables that have strong negative linear correlation.

(b) Explain in your own words why the linear correlation coefficient should not be used when its absolute value is too low or close to zero. Give an example.

(c) In the passage below identify the explanatory variable and the response variable. Explain why.
A nutritionist wants to determine if the amounts of water consumed each day by persons of the same weight and on the same diet can be used to predict individual weight loss.

(a) A strong positive linear correlation is observed when one variable increases as the increase in another variable happens linearly.
The variables rate of smoking and alcohol use shows a strong positive linear correlation. As the alcohol use increases, the rate of smoking also increases.
A strong negative linear correlation is observed when one variable increase but the decrease in another variable happens linearly.
The variables amount of playing games each week and GPA of students are strongly negative linear correlation because the more amount students spent in playing games each week, the GPA’s decreases.

(b) When the absolute value of the linear correlation coefficient is too low or close to zero, it shouldn’t be used. It indicates that there is no correlation between the variables, there is no relationship, interdependence, or connection between the variables.
It shows that the variables have nothing to do with each other and use of such variables makes no sense.
The variables, the amount of tea drunk and level of intelligence shows zero correlation.

(c) Explanatory or independent variable: Amount of water consumed each day because it is not depending on any other factor or variable.
Response or dependent variable: Weight loss because the variable weight loss is depending on the amount of water consumed each day.

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