Can someone please also show me the workings as I would like to see how this is
ID: 3331060 • Letter: C
Question
Can someone please also show me the workings as I would like to see how this is done. Thank You
2-The following data is the results of a 4- year study conducted to assess how age, weight, and gender influence the risk of diabetes. Risk is interpreted as the probability (times 100) that the patient will have diabetes over the next 4-year period.
a )Develop an estimated multiple regression model that relates risk of diabetes to the person’s age, weight, and the gender. Present the regression formula as a mathematical equation. Interpret the coefficients of the regression and comment on the strength of the regression.
b) What is the risk percentage of diabetes over the next 4 years for a 55-year-old man with 65 kg weight?
Age
Weight (Kg)
Gender
Risk (%)
53
78
1
40
24
77
0
23
77
83
1
67
88
89
1
71
56
65
0
45
71
82
1
54
53
79
1
48
70
66
0
49
80
80
1
65
78
67
0
59
71
69
0
56
70
78
1
59
67
75
0
46
77
95
1
64
60
57
0
39
82
100
1
73
66
85
0
63
80
96
0
87
62
83
1
52
59
93
0
61
Age
Weight (Kg)
Gender
Risk (%)
53
78
1
40
24
77
0
23
77
83
1
67
88
89
1
71
56
65
0
45
71
82
1
54
53
79
1
48
70
66
0
49
80
80
1
65
78
67
0
59
71
69
0
56
70
78
1
59
67
75
0
46
77
95
1
64
60
57
0
39
82
100
1
73
66
85
0
63
80
96
0
87
62
83
1
52
59
93
0
61
Explanation / Answer
a )Develop an estimated multiple regression model that relates risk of diabetes to the person’s age, weight, and the gender. Present the regression formula as a mathematical equation. Interpret the coefficients of the regression and comment on the strength of the regression.
Ans:
Output of the analysis
> Chegg=read.csv("Chegg_CSV.csv", sep=",", header=T)
>
> model=lm( Risk~ Age+ Weight+factor(Gender), data=Chegg)
> summary(model)
Call:
lm(formula = Risk ~ Age + Weight + factor(Gender), data = Chegg)
Residuals:
Min 1Q Median 3Q Max
-9.6735 -3.2769 0.1316 2.5482 8.7716
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -40.0367 8.7217 -4.590 0.000302 ***
Age 0.7368 0.0819 8.997 1.17e-07 ***
Weight 0.6179 0.1092 5.658 3.56e-05 ***
factor(Gender)1 -5.5357 2.3918 -2.314 0.034258 *
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 4.734 on 16 degrees of freedom
Multiple R-squared: 0.9061, Adjusted R-squared: 0.8885
F-statistic: 51.49 on 3 and 16 DF, p-value: 1.926e-08
The estimated multiple regression model that relates risk of diabetes to the person’s age, weight, and the gender is
diabetes= -40.0367 +0.7368 age+ 0.6179 weight - 5.5357 gender
Conclusion: All the estimated p-values of age, weight and gender are less than 0.05 level of significance. Hence, we can conclude that the these three variables have significant association with the risk of diabetes at 0.05 level of significance. For a unit increased on the age of the person the mean risk of the diabetes is increased by 0.7368. Similarly, for increased a unit on weight increases the mean diabetes by 0.6179 . Ans, the mean risk of diabetes is -5.5357 less when the gender is 1 compare to gender is 0.
b) What is the risk percentage of diabetes over the next 4 years for a 55-year-old man with 65 kg weight?
Ans: The risk percentage of diabetes over the next 4 years for a 55-year-old man with 65 kg weight is
diabetes= -40.0367 +0.7368 * 55+ 0.6179 * 65= 40.6508.