Variable Coefficient Std. Error t p Diet group -11.25 4.33 -2.60 0.01081 Baselin
ID: 3048280 • Letter: V
Question
Variable
Coefficient
Std. Error
t
p
Diet group
-11.25
4.33
-2.60
0.01081
Baseline cholesterol
0.85
0.07
12.14
<0.00001
BMI
0.23
0.65
0.35
0.727113
Gender
-3.02
4.42
-0.68
0.498158
1. In a study designed to examine the effects of adding oat bran to the typical American diet, 100 individuals were randomly divided into two different groups. Twice a day, the first group substituted oat bran for other food containing carbohydrates; the members of the second group did not make any changes to the diets. One outcome of interest was the serum cholesterol level of each individual eight weeks after the start of the study. Explanatory variables which might affect this response include diet group, serum cholesterol level at the start of the study, BMI, and gender. The estimated coefficients and standard errors are below (the intercept is not shown).
a. At the 0.05 level of significance, how many of the four explanatory variables have an effect on serum cholesterol level eight weeks after the start of the study, adjusting for the other variables? What are they?
Df = n-k-1 = 100-4-1 = 95
b. (4 points) If an individual’s baseline cholesterol were to increase by 20 mg/100 ml while the values of all other explanatory variables remain constant, what would happen to his or her serum cholesterol level eight weeks into the study?
(6 points) The indicator variable diet group is coded so that a 1 represents a member of the first group and 0 designates a member of the second group. Who is more likely to have a higher serum cholesterol level? By how much
Variable
Coefficient
Std. Error
t
p
Diet group
-11.25
4.33
-2.60
0.01081
Baseline cholesterol
0.85
0.07
12.14
<0.00001
BMI
0.23
0.65
0.35
0.727113
Gender
-3.02
4.42
-0.68
0.498158
Explanation / Answer
a variable is considered signficant for the model if its p value is less than the assumed alpha. Here the p values of BMI and gender is not less than 0.05 , hence both these variables are not signficant for the model
Only Dietgroup and cholestrol are significant
b)
we see that the coeffiecnt of baseline cholestrol is
0.85
Hence if the value of cholestrol changes by 20 mg
then the value of the depednent variable would increase by
0.85*20 = 17
the coeffiecient of diet group is
Diet group
-11.25
where 1 indicates the rpesence of 1st group
Hence 2nd group is likely to have higher serum level , by atleast 11.25 units keeping other values as constant
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