Use the following data provided to find the BEST possible regression equation:
x= 4,10,18,24,29,34,36,42
y= 1.5,2,1,3.5,4,3,2.5,2.5
The best possible regression equation would be the equation of a straight line. To find the equation of the straight line that best fits the data, you can use linear regression analysis.
The equation of a straight line is y = mx + b, where m is the slope of the line and b is the y-intercept.
Using the data provided, we can calculate the mean values of x and y:
Mean of x = (4 + 10 + 18 + 24 + 29 + 34 + 36 + 42) / 8 = 23.125
Mean of y = (1.5 + 2 + 1 + 3.5 + 4 + 3 + 2.5 + 2.5) / 8 = 2.625
Next, we calculate the slope (m) of the line using the formula:
m = Σ((x - mean of x) * (y - mean of y)) / Σ((x - mean of x)^2)
m = (30.875) / 470.875 ≈ 0.0656
Now we can calculate the y-intercept (b) using the formula:
b = mean of y - (m * mean of x)
b = 2.625 - (0.0656 * 23.125) ≈ 1.0255
Therefore, the best possible regression equation for the data provided is:
y ≈ 0.0656x + 1.0255