Write an equation for a line of best fit for the data in the table below.
Sandwich Total Fat Total Cals.
Hamburger 9 260
Cheeseburger 13 320
Quarter Pounder 21 420
Quarter w/cheese 30 530
To find the equation for the line of best fit, you can use linear regression. This statistical technique calculates the equation of a straight line that best fits the given data points.
First, let's assign the variables:
- x represents the Total Fat
- y represents the Total Calories
Now, we need to calculate the slope (m) and the y-intercept (b) using the linear regression equation:
m = (n∑xy - ∑x∑y) / (n∑x² - (∑x)²)
b = (∑y - m∑x) / n
Where:
- n is the number of data points.
- ∑xy is the sum of the product of x and y values.
- ∑x is the sum of the x values.
- ∑y is the sum of the y values.
- ∑x² is the sum of the squared x values.
Now, let's calculate the values needed for the equation:
n = 4 (since there are four data points)
∑xy = (9 * 260) + (13 * 320) + (21 * 420) + (30 * 530) = 43,470
∑x = 9 + 13 + 21 + 30 = 73
∑y = 260 + 320 + 420 + 530 = 1,530
∑x² = (9²) + (13²) + (21²) + (30²) = 1,651
Using these values, we can calculate the slope (m) and the y-intercept (b):
m = (4 * 43,470 - 73 * 1,530) / (4 * 1,651 - 73²) = 238.2 / 254 = 0.937007874
b = (1,530 - 0.937007874 * 73) / 4 = 1,530 - 68.32283465 / 4 = 1,461.674466 / 4 = 365.4186165
Therefore, the equation for the line of best fit is:
y = 0.937007874x + 365.4186165
In this equation, x represents the Total Fat, and y represents the Total Calories.