Anyone know how to get me started?
Calculate b0 and b1 and make an equation of regression line
for the set of data given in Table 3
Table 3
x y
1 12
2 15
3 16
5 18
6 21
8 23
If you need to show the work by hand, you can develop the regression equation in the following format:
predicted y = a + bx
...where a represents the y-intercept and b the slope.
To get to that point, here are some formulas to calculate along the way.
To find a:
a = (Ey/n) - b(Ex/n)
Note: E means to add up or to find the total.
To find b:
b = SSxy/SSxx
To find SSxy:
SSxy = Exy - [(Ex)(Ey)]/n
To find SSxx:
SSxx = Ex^2 - [(Ex)(Ex)]/n
I hope this will help get you started.
Thank you!!!
To calculate b0 and b1, we can use the formula for simple linear regression:
b1 = (nΣxy - ΣxΣy) / (nΣx^2 - (Σx)^2)
b0 = (Σy - b1Σx) / n
First, let's calculate the necessary sums:
Σx = 1 + 2 + 3 + 5 + 6 + 8 = 25
Σy = 12 + 15 + 16 + 18 + 21 + 23 = 105
Σxy = (1*12) + (2*15) + (3*16) + (5*18) + (6*21) + (8*23) = 686
Σx^2 = (1^2) + (2^2) + (3^2) + (5^2) + (6^2) + (8^2) = 155
Now, substitute these values into the formulas:
n = 6 (since we have 6 data points)
b1 = (6*686 - 25*105) / (6*155 - 25^2)
= 111 / -19
= -5.8421
b0 = (105 - (-5.8421)*25) / 6
= 79.4211
So the equation of the regression line is:
y = -5.8421x + 79.4211
This equation represents the linear relationship between x and y based on the given data.