Part of a study to determine factors influencing family medical expenses involve
ID: 3226734 • Letter: P
Question
Part of a study to determine factors influencing family medical expenses involves finding a regression relationship between the number of people in a family and the monthly medical expense. The data for the pilot study is located in the MEDICAL tab in the Excel file provided.
a). Develop a regression model at the .05 level of significance.
b). What can be said regarding the slope and correlation coefficient? Conduct the (t)-test for the correlation coefficient.
c). Use your results in (a) to determine the monthly medical expenses for a family of (4)? Is this meaningful?
d). Use your results in (a) to determine the monthly medical expenses for single person household? Is this meaningful?
Family Size Monthly Expenses 3 85 2 75 3 80 5 120 4 95 5 100 6 130 8 165Explanation / Answer
Part-a
Results are as follows from where estimated model is
Monthly expenses=37.01923077 + 15.38461538 Family size
SUMMARY OUTPUT
Regression Statistics
Multiple R
0.973945447
R Square
0.948569735
Adjusted R Square
0.939998024
Standard Error
7.457142506
Observations
8
ANOVA
df
SS
MS
F
Significance F
Regression
1
6153.846154
6153.846154
110.6628242
4.33576E-05
Residual
6
333.6538462
55.60897436
Total
7
6487.5
Coefficients
Standard Error
t Stat
P-value
Lower 95%
Upper 95%
Intercept
37.01923077
7.089566813
5.221649185
0.001973044
19.67168572
54.36677582
Family Size
15.38461538
1.462465968
10.51963993
4.33576E-05
11.80609008
18.96314069
Part-b
Slope is significant with p= 0.00004<0.05
As slope is significant so correlation is also significant.
Part-c
The monthly medical expenses for a family of (4)
=37.01923077 + 15.38461538 *4
=98.55769229
This is meaningful as 4 is within range of given data
Part-d
The monthly medical expenses for a family of (1)?
=37.01923077 + 15.38461538 *1
=52.40384615
SUMMARY OUTPUT
Regression Statistics
Multiple R
0.973945447
R Square
0.948569735
Adjusted R Square
0.939998024
Standard Error
7.457142506
Observations
8
ANOVA
df
SS
MS
F
Significance F
Regression
1
6153.846154
6153.846154
110.6628242
4.33576E-05
Residual
6
333.6538462
55.60897436
Total
7
6487.5
Coefficients
Standard Error
t Stat
P-value
Lower 95%
Upper 95%
Intercept
37.01923077
7.089566813
5.221649185
0.001973044
19.67168572
54.36677582
Family Size
15.38461538
1.462465968
10.51963993
4.33576E-05
11.80609008
18.96314069
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