Your research the average cost of whole milk for several years to look for trends the table shows your data what is the equation for a line of best fit how much would you expect to pay for a gallon of milk in the year 2023

Year, 1998, 2000, 2002, 2004, 2006, 2008
Cost, 2.58, 2.76, 2.94, 2.91, 3.19, 3.72
Milk can you show me how to figure it out and explain thank you

since 2003 is half-way between 2002 and 2004, its cost will be half-way between the costs for those years.

by the way, the number half-way from a to b is a + (b-a)/2 = (a+b)/2, the average of a and b.

To find the equation for a line of best fit, you can use the method of least squares. This involves minimizing the sum of the squares of the differences between the actual data points and the corresponding points predicted by the line.

1. First, let's assign the "Year" values as the independent variable, denoted as x, and the "Cost" values as the dependent variable, denoted as y.

2. Next, calculate the means for both x (x̄) and y (ȳ). The mean is found by summing all values and dividing by the total number of values.

x̄ = (1998 + 2000 + 2002 + 2004 + 2006 + 2008) / 6 = 2004
ȳ = (2.58 + 2.76 + 2.94 + 2.91 + 3.19 + 3.72) / 6 = 3.06

3. Subtract the means from each respective data point (x - x̄ and y - ȳ) to get the deviations.

Year Deviation (x - x̄): -6, -4, -2, 0, 2, 4
Cost Deviation (y - ȳ): -0.48, -0.3, -0.12, -0.15, 0.13, 0.66

4. Calculate the product of the deviations for each data point (x - x̄) * (y - ȳ).

Product: 2.88, 1.2, 0.24, -0, 0.26, 2.64

5. Calculate the squared deviations for x and y, as well as the sum of the squared deviations.

Square of x deviations: 36, 16, 4, 0, 4, 16
Square of y deviations: 0.2304, 0.09, 0.0144, 0.0225, 0.0169, 0.4356
Sum of squared deviations of x: 76
Sum of squared deviations of y: 0.8098

6. Calculate the sum of the product of x deviations and y deviations.

Sum of (x - x̄) * (y - ȳ): 7.22

7. Now, we can calculate the slope (b) of the line of best fit using the following formula:

b = Sum of (x - x̄) * (y - ȳ) / Sum of squared deviations of x

b = 7.22 / 76 ≈ 0.095

8. Finally, we can calculate the y-intercept (a) of the line using the formula:

a = ȳ - b * x̄

a = 3.06 - 0.095 * 2004 ≈ -100.68

The equation for the line of best fit is y = 0.095x - 100.68

To estimate the cost of a gallon of milk in the year 2023, substitute x = 2023 into the equation:

y = 0.095 * 2023 - 100.68 ≈ 108.72 (rounded to two decimal places)

Therefore, you can expect to pay approximately $108.72 for a gallon of milk in the year 2023 based on the line of best fit.

2.54x+0.098;$4.98