Case 9: Fat Consumption and Prostate Cancer Researchers have asked if there is a
ID: 3360598 • Letter: C
Question
Case 9: Fat Consumption and
Prostate Cancer
Researchers have asked if there is a relationship between nutrition and cancer, and many studies have shown that there is. In fact, one of the conclusions of study conducted by B. Reddy et al. (“Nutrition and its Relationship to Cancer,” Advances in Cancer Research, 32, pp.237-345) was that “…none of the risk factors for cancer is probably more significant than diet and nutrition.”
Prostate cancer is one of the most virulent forms of cancer. One dietary factor that has been studied for its relationship with prostate cancer is fat consumption. The data in the following table were obtained from a graph-adapted from information in the aforementioned article-in John Robbin’s classic book Diet for a New America (Walpole, NH: Stillpoint Publishing, 1987).
Country
Dietary fat
(grams/day)
Death rate
(per 100,000)
Country
Dietary fat
(grams/day)
Death rate
(per 100,000)
El Salvador
38
0.9
Spain
97
10.2
Philippines
29
1.3
Portugal
73
11.4
Japan
42
1.6
Finland
112
11.1
Mexico
57
4.5
Hungary
100
13.1
Greece
96
4.8
United Kingdom
143
12.4
Colombia
47
5.4
Germany
134
12.9
Bulgaria
67
5.5
Canada
142
13.4
Yugoslavia
72
5.6
Austria
119
13.9
Poland
93
6.4
France
137
14.4
Panama
58
7.8
Netherlands
152
14.4
Israel
95
8.4
Australia
129
15.1
Romania
67
8.8
Denmark
156
15.9
Venezuela
62
9.0
United States
147
16.3
Czechoslovakia
96
9.1
Norway
133
16.3
Italy
86
9.4
Sweden
132
18.4
1. Draw a scatter diagram for the data on dietary fat and prostate cancer death rate. What does the scatter diagram tell you?
2. Does it appear reasonable to obtain a regression equation for the data? Explain your answer.
3. Find the regression equation for the data using dietary fat as the predictor variable.
4. Interpret the slope of the regression line.
5. Compute the correlation coefficient of the data and interpret your result.
Identify outliers, if any.
_______
Case 9: Fat Consumption and
Prostate Cancer
Explanation / Answer
1…….Let Y=Deathrate and X=Dietaryfat then the scatterplot is
2……..Now By observing the scatter plot we can say that there is a positive relation between the dietary fat and the prostate cancer i.e. the more is the fat in the diet the chances of prostate cancer is more.Hence it is reasonable to obtain regression equation for the data.
3………To find the regression equation we use least squares method.
Simple Linear regression model of our data
Y=b0+b1+e where e is the statistical error follows normal distribution with mean 0 ad variance sigma^2
And
Here b0 and b1 are intercept and slope respectively.
sum(y)= 297.7
sum(x)=2911
mean(x)=97.03333
mean(y)=9.923333
sum(xy)=33573.3
sum(x^2)=323963
sxy= 4686.477
sxx= 41498.97
b1= 0.11293
b0=-1.034637
4….Now the value of the slope is 0.11293 i.e this is the change in the value of y corresponding to unit change in the value of x.
5…..The correlation coefficient is
This gives the value of r=0.8860299. Hence there is positive relation between the dietary fat and prostate cancer. We can interpret that the more consumption of fat in the diet leads to more chances of causing prostate cancer.
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