Question

60 observations from a study on the impact of exercise and diet on body weight loss. The variables, exercise, diet, and exdiet are binary variables and the variable diff is a continuous variable. All of these are defined as follows:

exercise = 1 if a person exercises, 0 otherwise
diet = 1 if a person follows a diet plan, 0 otherwise
exdiet = 1 if a person exercises and follows a diet plan, 0 otherwise
diff = The difference observed in weight (in lbs.) after 3 months of observation. Positive numbers indicate weight loss and negative numbers indicate weight gain.

Based on this information, you are required to answer the following questions:

Here are the summary statistics for all four variables and discuss what they indicate.

	Exercise	diet	Exdiet	diff
count	60	60	60	60
mean	0.68	0.48	0.45	10.595932
sample standard deviation	0.47	0.50	0.50	9.771008
sample variance	0.22	0.25	0.25	95.472603
minimum	0	0	0	-16.2738
maximum	1	1	1	26.5177
range	1	1	1	42.7915
1st quartile	0.00	0.00	0.00	4.075273
median	1.00	0.00	0.00	11.387700
3rd quartile	1.00	1.00	1.00	18.964165
interquartile range	1.00	1.00	1.00	14.888892
mode	1.00	0.00	0.00	#N/A
low extremes	0	0	0	0
low outliers	0	0	0	0
high outliers	0	0	0	0
high extremes	0	0	0	0

There is no meaningful interpretation of the first three variables because they are dummy variables.

The fourth variable has a greater variance.

There are no outliers in the data.

Do a regression analysis on this dataset after identifying a dependent variable and one or more independent variables…

If only one independent variable, is the model reliable? Why?
If more than one independent variable, is the model better? Why?
The relationship between exercise and weight loss and between diet and weight loss?
The relationship between exercise and diet together and weight loss?
The relationships described in (c.) and (d.) significant or not? Why?

Answer 1

Do a regression analysis on this dataset after identifying a dependent variable and one or more independent variables

There are only one dependent variable and three independent variables.

If only one independent variable, is the model reliable? Why?

No, because dummy variables have no significance.
If more than one independent variable, is the model better? Why?

No, because dummy variables have no significance.
The relationship between exercise and weight loss and between diet and weight loss?

The regression output is:

	exercise	diet	exdiet
exercise	1.000
diet	.515	1.000
exdiet	.616	.935	1.000

There is a relationship between exercise and weight loss and between diet and weight loss.

The relationship between exercise and diet together and weight loss?

There is a relationship between exercise and diet together and weight loss.
The relationships described in (c.) and (d.) significant or not? Why?

There is a significant relationship between the variables in (c.) and (d.).