what is the function if x is 3,0,7,5 and the y being 16,10,24,20?
To find the function that relates x and y, we can use the method of regression analysis. This method helps us determine the equation of the line that best fits the given data points (x, y values). The equation of the line will represent the function we are looking for.
To begin, let's list the given data points:
x: 3, 0, 7, 5
y: 16, 10, 24, 20
Step 1: Calculating the Mean of x and y:
First, we need to calculate the mean (average) of both x and y.
The mean of x: (3+0+7+5)/4 = 3.75
The mean of y: (16+10+24+20)/4 = 17.5
Step 2: Calculate the deviations:
Next, we need to calculate the deviation of each x value from the mean of x and the deviation of each y value from the mean of y.
Deviation of x: (3-3.75), (0-3.75), (7-3.75), (5-3.75) = -0.75, -3.75, 3.25, 1.25
Deviation of y: (16-17.5), (10-17.5), (24-17.5), (20-17.5) = -1.5, -7.5, 6.5, 2.5
Step 3: Calculate the product of deviations:
Multiply each deviation of x by the corresponding deviation of y.
Product of deviations: (-0.75 * -1.5), (-3.75 * -7.5), (3.25 * 6.5), (1.25 * 2.5) = 1.125, 28.125, 21.125, 3.125
Step 4: Calculate the squared deviations of x:
Square each deviation of x.
Squared deviations of x: (-0.75)^2, (-3.75)^2, (3.25)^2, (1.25)^2 = 0.5625, 14.0625, 10.5625, 1.5625
Step 5: Calculate the equation coefficients:
Now, we can calculate the coefficients of the equation using the following formulas:
Slope (b) = Σ((x - mean of x) * (y - mean of y)) / Σ((x - mean of x)^2)
Intercept (a) = mean of y - (slope * mean of x)
Using these formulas, we calculate:
b = Σ(product of deviations) / Σ(squared deviations of x) = (1.125+28.125+21.125+3.125) / (0.5625+14.0625+10.5625+1.5625) ≈ 2.018
a = mean of y - (slope * mean of x) = 17.5 - (2.018 * 3.75) ≈ 9.045
Therefore, the function that relates x and y is:
y = 2.018x + 9.045