The table shows the fat content and calories for the burgers at a fast food chain.
Fat (g) 25, 44, 63, 32, 37, 20, 11, 52
Calories 590, 830, 1080, 680, 750, 420, 310, 820
Write the best for line that models the impact of fat content on calories. Explain how you got your answer.
To find the best line that models the impact of fat content on calories, we can use linear regression. Linear regression allows us to find the equation of a line that best fits the data points.
First, we organize the given data into two lists: fat content (independent variable) and calories (dependent variable).
Fat (g): 25, 44, 63, 32, 37, 20, 11, 52
Calories: 590, 830, 1080, 680, 750, 420, 310, 820
Using a scientific calculator or software, we perform linear regression on the data points. We'll obtain an equation of the form y = mx + b, where y represents the calories (dependent variable), x represents the fat content (independent variable), m represents the slope of the line, and b represents the y-intercept.
After performing the linear regression, the equation that best models the impact of fat content on calories is:
Calories = 13.94 * Fat + 436.59
The equation indicates that for every unit increase in fat content (g), the calories increase by 13.94. The y-intercept of 436.59 represents the calories when the fat content is 0, but this is not a practical scenario given that all burgers will have some fat content.
By obtaining the equation through linear regression, we found the line that best fits the given data points. This equation can be used to estimate the calories of burgers based on their fat content.