Energy-drink advertising consistently emphasizes a physically active lifestyle a
ID: 3312943 • Letter: E
Question
Energy-drink advertising consistently emphasizes a physically active lifestyle and often features extreme sports and risk taking. Are these typical characteristics of an energy-drink consumer? A researcher decided to examine the links between energy-drink consumption, sport-related (jock) identity, and risk taking.5 She invited over 1500 undergraduate students enrolled in large introductory-level courses at a public university to participate. Each participant had to complete a 45-minute anonymous questionnaire. From this questionnaire jock identity and risk-taking scores were obtained, where the higher the score, the stronger the trait. She ended up with 795 respondents. The following table summarizes the results of a multiple regression analysis using the frequency of energy-drink consumption in the past 30 days as the response variable:
Explanatory variable
b
Age
0.02
Sex (1 = female, 0 = male)
0.11**
Race (1 = nonwhite, 0 = white)
0.02
Ethnicity (1 = Hispanic, 0 = non-Hispanic)
0.10**
Parental education
0.02
College GPA
0.01
Jock identity
0.05
Risk taking
0.19***
A superscript of ** means that the individual coefficient t test had a P-value less than 0.01, and a superscript of *** means that the test had a P-value less than 0.001. All other P-values were greater than 0.05.
(a) The overall F statistic is reported to be 8.11. What are the degrees of freedom associated with this statistic?
(b) R2 is reported to be 0.28. What percent of the variation in energy-drink consumption is explained by the model? Is this a highly predictive model? Explain.
(c) Interpret each of the regression coefficients that are significant.
Explanatory variable
b
Age
0.02
Sex (1 = female, 0 = male)
0.11**
Race (1 = nonwhite, 0 = white)
0.02
Ethnicity (1 = Hispanic, 0 = non-Hispanic)
0.10**
Parental education
0.02
College GPA
0.01
Jock identity
0.05
Risk taking
0.19***
Explanation / Answer
a) The degrees of freedom of this statistics are ( 7, 787).
b) 28 percent of the variation in energy-drink consumption is explained by the model.
No it is not highly predictive.
R-square or coefficient of determination of .28 is very less.
c)
Interpretation of coefficient :
sex (female) : a unit increase in sex(female) with respect to male, the energy-drink consumption decreases by -.11 keeping all other varibales constant.
Ethinicity (Hispanic) : a unit increase in Ethinicity (Hispanic) with respect to Non-Hispanic, the energy-drink consumption increases by 0.10 keeping all other varibales constant.
Risk taking : a unit increase in risk taking, the energy-drink consumption incraeses by 0.19 keeping all other varibales constant.
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