We wish to determine if there is a correlation between the birth weight (in grams) of nine newborn infants and the length of their mothers’ stay (in days) in the hospital. The results of a correlation and regression analysis are indicated in the Excel output below. The mean birth weight of the newborn infants (the independent variable) was 3162.5 grams, and the mean length of their mothers’ stay in the hospital (the dependent variable) was 7 days. SUMMARY OUTPUT Regression Statistics Multiple R 0.862675 R Square 0.744208 Adjusted R Square 0.707666 Standard Error 6.02142 Observations 9 ANOVA df SS MS F Significance F Regression 1 738.4198 738.4198 20.36599 0.002756 Residual 7 253.8025 36.25749 Total 8 992.2222 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept 34.99212 6.636627 5.272576 0.001157 19.29899 50.68525 19.29899 50.68525 BIRTH WEIGHT -0.00905 0.002005 -4.51287 0.002756 -0.01379 -0.00431 -0.01379 -0.00431 Part A: Using an alpha = 0.05, test the claim that there is a significant linear correlation between the birth weight of the newborn infants and the length of their mothers’ hospital stay. Part B: If the birth weight of a newborn infant is 3,000 grams, what is the best predicted length of their mothers’ hospital stay (in days)?
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.
- We wish to determine if there is a
correlation between the birth weight (in grams) of nine newborn infants and the length of their mothers’ stay (in days) in the hospital. The results of acorrelation and regression analysis are indicated in the Excel output below. The mean birth weight of the newborn infants (the independent variable) was 3162.5 grams, and the mean length of their mothers’ stay in the hospital (the dependent variable) was 7 days.
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SUMMARY OUTPUT |
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Regression Statistics |
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Multiple R |
0.862675 |
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R Square |
0.744208 |
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Adjusted R Square |
0.707666 |
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Standard Error |
6.02142 |
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Observations |
9 |
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ANOVA |
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df |
SS |
MS |
F |
Significance F |
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Regression |
1 |
738.4198 |
738.4198 |
20.36599 |
0.002756 |
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Residual |
7 |
253.8025 |
36.25749 |
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Total |
8 |
992.2222 |
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|
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Coefficients |
Standard Error |
t Stat |
P-value |
Lower 95% |
Upper 95% |
Lower 95.0% |
Upper 95.0% |
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Intercept |
34.99212 |
6.636627 |
5.272576 |
0.001157 |
19.29899 |
50.68525 |
19.29899 |
50.68525 |
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BIRTH WEIGHT |
-0.00905 |
0.002005 |
-4.51287 |
0.002756 |
-0.01379 |
-0.00431 |
-0.01379 |
-0.00431 |
Part A: Using an alpha = 0.05, test the claim that there is a significant
Part B: If the birth weight of a newborn infant is 3,000 grams, what is the best predicted length of their mothers’ hospital stay (in days)?
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