To determine the strength of the correlation between fat content (g) and calories in the burgers, you can calculate the Pearson correlation coefficient (r). This coefficient quantifies the degree of linear association between two variables, in this case, fat content and calories.
Steps to Calculate the Correlation Coefficient (r):
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Collect your data: Organize the fat content and calorie values into paired observations.
| Fat (g) | Calories | |---------|----------| | 25 | 590 | | 44 | 830 | | 63 | 1080 | | 32 | 680 | | 37 | 750 | | 20 | 420 | | 11 | 310 | | 52 | 820 |
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Calculate the means of the fat and calorie values.
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Calculate the covariance between the two variables.
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Calculate the standard deviations of both variables.
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Use the formula for the Pearson correlation coefficient:
\[ r = \frac{Cov(X, Y)}{SD_X \times SD_Y} \]
where \( Cov(X, Y) \) is the covariance between fat (X) and calories (Y), and \( SD_X \) and \( SD_Y \) are the standard deviations of fat and calories, respectively.
Interpretation of the Correlation Coefficient (r):
- r ranges from -1 to 1:
- r = 1: Perfect positive correlation (as fat increases, calories also increase).
- r = -1: Perfect negative correlation (as fat increases, calories decrease).
- r = 0: No correlation (no linear relationship between fat and calories).
The strength of the correlation can be categorized as:
- 0.00 - 0.19: Very weak
- 0.20 - 0.39: Weak
- 0.40 - 0.59: Moderate
- 0.60 - 0.79: Strong
- 0.80 - 1.00: Very strong
Conclusion:
Once you calculate the value of \( r \), you can conclude the strength and direction of the relationship between fat content and calories in the burgers. If \( r \) is high and positive, it indicates that higher fat content is associated with more calories. If \( r \) is low or negative, it suggests that there is little to no relationship.