Using a sample of 46 college students, we want to determine if there is a significant correlation between weight (in lbs.) and weekly exercise (in minutes). The results of a correlation and regression analysis are indicated in the Excel output below. The mean weight (the independent variable) was 166.80 lbs., and the mean weekly exercise time (the dependent variable) was 158.83 minutes. SUMMARY OUTPUT Regression Statistics Multiple R 0.027082077 R Square 0.000733439 Adjusted R Square -0.021977165 Standard Error 79.41761298 Observations 46 ANOVA df SS MS F Significance F Regression 1 203.6896 203.6896 0.032295 0.858207 Residual 44 277514.9 6307.157 Total 45 277718.6 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept 149.0807975 55.47825 2.687194 0.010131 37.27174 260.8899 Weight 0.058423474 0.325102 0.179708 0.858207 -0.59678 0.713624 Respond to Parts a and b below: Part A: Test the claim that there is a significant linear correlation between weight (in lbs.) and weekly exercise (in minutes). Part B: If a college student’s weight is 150 lbs., what is the best predicted weekly exercise time (in minutes) for this college student?
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.
- Using a sample of 46 college students, we want to determine if there is a significant
correlation between weight (in lbs.) and weekly exercise (in minutes). The results of acorrelation and regression analysis are indicated in the Excel output below. Themean weight (the independent variable) was 166.80 lbs., and the mean weekly exercise time (the dependent variable) was 158.83 minutes.
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SUMMARY OUTPUT |
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Regression Statistics |
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Multiple R |
0.027082077 |
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|
R Square |
0.000733439 |
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|
Adjusted R Square |
-0.021977165 |
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|
Standard Error |
79.41761298 |
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Observations |
46 |
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ANOVA |
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df |
SS |
MS |
F |
Significance F |
|
|
Regression |
1 |
203.6896 |
203.6896 |
0.032295 |
0.858207 |
|
|
Residual |
44 |
277514.9 |
6307.157 |
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Total |
45 |
277718.6 |
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|
|
|
|
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Coefficients |
Standard Error |
t Stat |
P-value |
Lower 95% |
Upper 95% |
|
Intercept |
149.0807975 |
55.47825 |
2.687194 |
0.010131 |
37.27174 |
260.8899 |
|
Weight |
0.058423474 |
0.325102 |
0.179708 |
0.858207 |
-0.59678 |
0.713624 |
Respond to Parts a and b below:
Part A: Test the claim that there is a significant
Part B: If a college student’s weight is 150 lbs., what is the best predicted weekly exercise time (in minutes) for this college student?
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