The following model is a simplified version of the multiple regression model used by Biddle and Hamermesh (1990) to study the tradeoff between time spent sleeping and working and to look at other factors affecting sleep:
sleep=B_0+B_1 totwork+B_2 educ+B_3 age+u
Where sleep and totwork(total work) are measured in minutes per week and educ and age are measured in years.
If adults trade off sleep for work what is the sign of B_1?
What signs do you think of B_2and B_3?
Suppose the estimated equation is;
(sleep) ̂=3638.25-0.148totwork-11.13educ+2.20age
n=706 and R^2= 0.113
If someone works five more hours per week, by how many minutes sleep is predicted to fall? Is this a large trade off?
Discuss the sign and magnitude of the estimated coefficient on educ
Would you say, totwork, educand age explain much of the variation in sleep? What other factor affect the time spent sleeping? Are these likely to be correlated withtotwork?
To answer these questions, we will analyze the given multiple regression model and the estimated equation. Let's break it down step by step:
1. Sign of B_1 (coefficient for totwork):
In the model, totwork represents the total work in minutes per week. If adults trade off sleep for work, we would expect a negative relationship between sleep and totwork. This means that as the total work increases, the predicted sleep would decrease. Therefore, the sign of B_1 should be negative.
2. Signs of B_2 and B_3 (coefficients for educ and age):
The coefficients B_2 and B_3 represent the impact of education (educ) and age on sleep, respectively. Without any additional information, it is challenging to predict the signs of these coefficients. However, based on general assumptions, we can make some educated guesses. Education may be positively related to sleep, as individuals with higher education levels often have better self-care practices. On the other hand, age may be negatively related to sleep as older individuals tend to experience more sleep disturbances. Therefore, we can hypothesize that B_2 might be negative, and B_3 might be positive. However, we cannot determine the signs definitively without further analysis.
3. Predicting the impact of increased work on sleep:
In the given estimated equation:
(sleep) ̂= 3638.25 - 0.148totwork - 11.13educ + 2.20age
If someone works five more hours per week, we can substitute totwork with the new value (increased by 5 * 60 minutes) and calculate the predicted change in sleep. So, let's calculate it:
Predicted sleep change = -0.148 * (5 * 60)
= -44.4 minutes
The negative sign indicates that with five more hours of work per week, the predicted sleep would decrease by 44.4 minutes. Whether this is considered a large tradeoff would depend on individual preferences and what is deemed significant in the context of sleep and work.
4. Discussing the coefficient on educ:
The estimated coefficient on educ (-11.13) suggests that, on average, each additional year of education is associated with a decrease in sleep by 11.13 minutes per week. The negative sign indicates an inverse relationship between education and sleep duration. It is important to note that this is just an association found in the data, and other factors may be influencing this relationship as well.
5. Variance explained and other factors affecting sleep:
To assess the extent to which totwork, educ, and age explain variation in sleep, we look at the coefficient of determination (R^2). In this case, R^2 is 0.113, which means that around 11.3% of the variation in sleep can be explained by the variables included in the model (totwork, educ, and age). This implies that there are other factors not included in the model that contribute to the remaining variation in sleep duration.
Other potential factors affecting sleep could include variables like health status, stress levels, lifestyle choices, sleep disorders, and individual differences in sleep needs. While these additional factors are not explicitly accounted for in the given model, they are likely to have an impact on sleep duration. Some of these factors may also be correlated with totwork, as work-related stress, for example, can influence both sleep patterns and the number of hours worked.
It is important to recognize that correlation does not imply causation, so further analysis and investigation would be necessary to establish the relationships and potential causal factors affecting sleep duration.