I need the solutions to all the parts with proper caculation Consider the case w
ID: 3050845 • Letter: I
Question
I need the solutions to all the parts with proper caculation
Consider the case where a multiple linear regression model predicting patient weight yields the following results. The variables are Age (in years), Gender(0=female, 1=male), fat intake (average daily intake where 1 = 10-19 g/day, 2=20-29 g/day, 3=30-39 g/day, etc), and exercise frequency (0= <5 days a week, 1= >5 days a week)
Variable
Parameter estimate
Standard error
t-value
Pr>|t|
Intercept
106.3
10.2
3.9
.003
Age
1.4
.36
7.5
<0.001
Gender
20.4
4.5
3.3
.01
Fat intake
3.8
5.6
.5
.70
Exercise
-10.7
2.8
6.7
0.001
P=0.0078
Adjusted R-square=0.48
a) Which variables should be included In the final model?
b) What is the predicted weight of a 35 year old male with fat intake=6 and exercise=1?
c) Why is fat intake not significant even though it has a higher coefficient than age?
d) What is the difference between the overall p-value and the individual p-values?
e) Based on the adjusted R-square of 0.48, is this a useful model to predict patient weight?
Variable
Parameter estimate
Standard error
t-value
Pr>|t|
Intercept
106.3
10.2
3.9
.003
Age
1.4
.36
7.5
<0.001
Gender
20.4
4.5
3.3
.01
Fat intake
3.8
5.6
.5
.70
Exercise
-10.7
2.8
6.7
0.001
P=0.0078
Adjusted R-square=0.48
Explanation / Answer
(a) Age, Gender and Excercise at 5% level of significance.
(b) The model is : y=106.3+ 1.4(Age)+20.4(Gender)+3.8 (Fat intake)-10.7(Exercise)
For the given values the predicted weight = 187.8.
(c) Since p-value for fat intake (0.70) is more than 0.05, Therefore it is not signifcantly effecting the weight at 5% level of significance. While p-value of age (<0.001)is less than 0.05. This implies age is significantly effectinf the weight at 5% level of significance.
(d) Overall p-value implies the sigificance of model and individual p-value shows significance of that particular variable. If overall p-value is less than 0.05 than model is signficant and could be used further. While if p-value of one or two variables is more than 0.05 implies that, that particular variable is not significance on dependent variable.
In this case overall p-value is 0.,0078. This implies model is significant. p-value of Fat intake is more than 0.05 implies it is not significantly effecting the weight.
(e) R-square =0.48 implies that this model is able to explain the relation between the variable only 48%. This is a moderate value. It is not too good model to predict patient weight.
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