Question

Question 9 

 Scenario:

 Two researchers in medicine and psychology are collaborating on a project in a sleep laboratory for two weeks. Each day participants were given different doses of vitamin D supplements and their daily minutes of sleep were controlled. The researchers were interested in the effect of the two independent variables on the daily number of minutes participants worked out for.

 The researchers agreed on the following equation for their statistical model:

 Y = b0 + b1 * X1 + b2 * X2 + b3 * X1 * X2

 Please specify the name of the analysis and the exact equation the researchers would use as a combination of mathematical term and actual variable names instead of the variable alphanumberic placeholders. As well, state how many effects you would expect to see in the model output and why.

 

Question 12 

 The researchers wisely go on to conducting model comparisons for all significant predictors shown in their model summary.

 Please explain why model comparisons are an essential part of regression analyses? As well, elaborate on the process of how you would conduct model comparisons for the analysis at hand, and what statistic/test you would use to make your judgement.

Answer 1

9)
This is multiple regression
daily number of minutes worked out^ = b0 + b1 * amount of dose of Vitamin D supplement + b2 * daily minutes of sleep + b3 * amount of dose of Vitamin D supplement * daily minutes of sleep

There are three effects , two main effects for amount of dose of Vitamin D supplement and daily minutes of sleep and one interaction term

12)
Model specification is the process of determining which independent variables to include and exclude from a regression equation
We have to choose the model which has better explanatory power/ better forecasting power depending on our needs.
Model comparisons allow us to decide which model is better, or which variable/ pair of variables are insignificant to dependent variable.
We can use t-tests for significance for individual variable and F-tests reduced model for joint significance of many variables.
Other criterion are possible like adjusted R^2 , AIC, BIC , Mallow’s CP etc
In Multiple regression, there are many methods forward selection, backward elimination or best subsets regression