To determine the correlation between fat content (g) and calories for the burgers, you need to calculate the Pearson correlation coefficient (r). This statistical measure quantifies the strength and direction of the linear relationship between two variables. Here's how to perform the calculation and interpret the results:
Steps to Calculate Pearson Correlation Coefficient (r):
-
Collect Data: You have the paired data for fat content and calories:
- Fat (g): [25, 44, 63, 32, 37, 20, 11, 52]
- Calories: [590, 830, 1080, 680, 750, 420, 310, 820]
-
Calculate Mean of Each Variable:
- Mean of Fat (g)
- Mean of Calories
-
Calculate the Covariance of the Two Variables: \[ \text{Cov(X,Y)} = \frac{1}{N-1} \sum (X_i - \bar{X})(Y_i - \bar{Y}) \]
-
Calculate the Standard Deviations of Each Variable: \[ s_X = \sqrt{\frac{1}{N-1} \sum (X_i - \bar{X})^2} \] \[ s_Y = \sqrt{\frac{1}{N-1} \sum (Y_i - \bar{Y})^2} \]
-
Calculate the Pearson Correlation Coefficient: \[ r = \frac{\text{Cov(X,Y)}}{s_X s_Y} \]
Interpretation of the Results:
- The correlation coefficient (r) ranges from -1 to 1.
- r = 1: Perfect positive linear correlation
- r = -1: Perfect negative linear correlation
- r = 0: No linear correlation
- 0 < r < 1: Positive correlation
- -1 < r < 0: Negative correlation
Final Steps:
Once you compute 'r', you can interpret its value:
- Values close to 1 indicate a strong positive correlation, meaning that as fat content increases, calorie content also tends to increase.
- Values close to -1 indicate a strong negative correlation, meaning that as one variable increases, the other tends to decrease.
- Values close to 0 suggest little to no linear correlation between the two variables.
To perform the calculations, you can use statistical software or a calculator. If you need the actual computed value, please let me know, and I'll help you with that calculation.
1 answer