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OPDRACHTEN TIJDENS SEMINARBlock GZW3024, Multiple linear regression, seminar 2, assignments
Assignment 1:
Below you find the results of a statistical analysis on data obtained for a cohort of health sciences
students at Maastricht University (N = 213). Registered were the students’ age, gender, whether they
smoked or not, but also their body length (in meters) and percentage of body fat. Gender is denoted in
the analysis as “gender” (0 = female; 1 = male) and body length as “length” and percentage of body
fat as “percfat”. Whenever required, use a significance level of 5%. The following results were
obtained in SPSS:
Variables Entered/Removeda
Variables Variables
Model Entered Removed Method
1 genderb . Enter
a. Dependent Variable: percfat
b. All requested variables entered.
Model Summary
Adjusted R Std. Error of
Model R R Square Square the Estimate
1 .817a .668 .666 4.02588
a. Predictors: (Constant), gender
ANOVAa
Sum of
Model Squares df Mean Square F Sig.
1 Regression 7331.768 1 7331.768 452.364 .000b
Residual 3646.726 225 16.208
Total 10978.494 226
a. Dependent Variable: percfat
b. Predictors: (Constant), gender
Coefficientsa
, Standardized
Unstandardized Coefficients Coefficients
Model B Std. Error Beta t Sig.
1 (Constant) 26.973 .311 86.841 .000
gender -12.958 .609 -.817 -21.269 .000
a. Dependent Variable: percfat
1. Write down the regression equation as estimated for the student sample:
Fatperc = 26, 975 -12,958* Gender + ei
, 2. The prediction equation is: ^
percfat = b0 + b1 gender
What are b0 and b1 in the analysis for the student sample?
B0 = 26, 975
B1 = -12,958
3. What is the predicted percentage of body fat for male students and what is the predicted
percentage of body fat for female students in terms of the general formulation of the prediction
equation in 2. ?
percfat = 26, 975 -12,958* Gender + ei
Female:
percfat = 26, 975 -12,958* 0 = 26
Male:
percfat = 26, 975 -12,958* 1 = 14
het verschil er tussen is de coefficient
In general:
Y^ male = b0 + b1* 1 = b0+b1
Y ^ female = b0 + b1 * 0 = b0
What are the predicted values for males, females and their difference based on the analysis results
for the sample?
4. What is your evaluation of the quality of the regression line? Explain your answer
Rkwadraad = 0,668.
Variatie in de uitkomstvariabelen kan worden verklaard door predictor variabelen.
66,8% of the variance is the outcome variables (percfat) can be explained by variance in the predictor
variables (gender). So, this regression line gives a reasonable description of the scatterplot.
5. For the analysis given above, write down the regression model for the population.
Percfat = B0 + B1 lenght + Ɛii
, 6. You would like to know whether there is a relation between gender and percfat in the population
of students. Formulate the null and the alternative hypothesis.
H0: B1 = 0
Ha: B1 ≠ 0
7. Report a statistical test statistic for these hypotheses. What value does it have, and what is the
corresponding p-value ?
8. Explain whether we should accept or reject the null hypothesis. Conclude whether there is or there is
no relation between gender and percfat in the population.
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