Both arm circumference and BMI measurements have been used as screening tools for being underweight, overweight, or obese. We want to determine if there is a significant correlation between arm circumference (in centimeters or cm) and body mass index or BMI (in kg.m2) among 10 participants. The results of a correlation and regression analysis are indicated in the Excel output below. The mean arm circumference (the independent variable) was 35.2 cm, and the mean BMI (the dependent variable) was 30.7 kg.m2. SUMMARY OUTPUT Regression Statistics Multiple R 0.855646 R Square 0.732129 Adjusted R Square 0.698646 Standard Error 3.806088 Observations 10 ANOVA df SS MS F Significance F Regression 1 316.7456 316.7456 21.86518 0.001590054 Residual 8 115.8904 14.4863 Total 9 432.636 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept -9.00956 8.581271 -1.04991 0.324438 -28.79801035 10.77888 ARM CIRC 1.129322 0.241514 4.676022 0.00159 0.572391244 1.686254 Part A: Using an alpha = 0.05, test the claim that there is a significant linear correlation between arm circumference (in centimeters or cm) and body mass index or BMI (in kg.m2). Part B: If the arm circumference (in centimeters or cm) for an adult is 37.5 cm, what is the best predicted BMI measurement in kg.m2?
Correlation
Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.
Linear Correlation
A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related.
Regression Analysis
Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.
Both arm circumference and BMI measurements have been used as screening tools for being underweight, overweight, or obese. We want to determine if there is a significant
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SUMMARY OUTPUT |
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Regression Statistics |
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Multiple R |
0.855646 |
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R Square |
0.732129 |
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Adjusted R Square |
0.698646 |
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Standard Error |
3.806088 |
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Observations |
10 |
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ANOVA |
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df |
SS |
MS |
F |
Significance F |
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Regression |
1 |
316.7456 |
316.7456 |
21.86518 |
0.001590054 |
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Residual |
8 |
115.8904 |
14.4863 |
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Total |
9 |
432.636 |
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Coefficients |
Standard Error |
t Stat |
P-value |
Lower 95% |
Upper 95% |
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Intercept |
-9.00956 |
8.581271 |
-1.04991 |
0.324438 |
-28.79801035 |
10.77888 |
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ARM CIRC |
1.129322 |
0.241514 |
4.676022 |
0.00159 |
0.572391244 |
1.686254 |
Part A: Using an alpha = 0.05, test the claim that there is a significant
Part B: If the arm circumference (in centimeters or cm) for an adult is 37.5 cm, what is the best predicted BMI measurement in kg.m2?
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