Question

3) If you wanted to determine whether there is a relationship between “the number of steps one walks during a given week” and “score on a neuroticism test” using the correlation method of research,

3a) Give one variable that would likely be positively correlated with “number of steps walked”.
3b) Give one variable that would likely be negatively correlated with “number of steps walked”. (Don’t use the same variables as in 3C)
3c) If the correlation coefficient between “number of steps walked” and “neuroticism” is
r = +.095, describe how these two variables are related.
3d) What is the coefficient of determination AND what is it telling you about how “number of steps” and “neuroticism” are related?

Answer 1

(a)

The level of health awareness of a person is likely to positively affect how much they indulge in physical activities. A person who is more health conscious, is likely to move around more, even while not exercising or going to the gym; they are the ones more likely to take the stairs instead of elevators, or park their vehicles one block away from their work-place.

Hence, the level of health awareness is a variable likely to be positively correlated with “number of steps walked”.

(b)

The Basal Metabolic Index (BMI) of a person is a parameter that measures whether a person has normal weight, is overweight, or is obese. Higher the BMI is, more is the person likely to be overweight or obese. A lower BMI-person is likely to be of normal weight. It can be observed that people with normal weights are the ones likely to move around more than those who are overweight or obese.

Hence, the BMI of a person is a variable likely to be negatively correlated with “number of steps walked”.

(c)

If the correlation is r = +0.95, which is very close to the perfect positive correlation value of +1, it would mean that the “number of steps walked” has a very strong positive correlation, that is, a very strong positive linear relationship with “neuroticism”.

(d)

For a simple regression mode, the coefficient of determination, R² is the same as r², that is, the square of the correlation coefficient.

Here, r² = (0.95)² = 0.9025.

This gives the proportion of variability in the response variable of the model (here, “number of steps walked”) that is explained by the explanatory variable (here, “neuroticism”).

Thus, about 0.9025 proportion or 90.25% of the variability in the “number of steps walked” is explained by “neuroticism”. Thus, the model with “neuroticism” as the explanatory variable fits the data on “number of steps walked” very well. This indicates a very strong linear relationship between the two variables.