Y x1 x2
57 220 125
43 216 147
73 250 118
37 241 160
64 305 128
48 258 149
354 145
56 150
321 140
50 370 115
39 375 155
43 385 152
64 385
60
calculate the fitted line regression
To calculate the fitted line regression, we can use the following formula:
y = b0 + b1x
Where y is the predicted value of Y, b0 is the y-intercept, b1 is the slope, and x is the independent variable.
First, let's calculate the slope (b1) of the regression line:
n = number of data points = 11
Σx1 = sum of all x1 values = 2,577
Σx2 = sum of all x2 values = 1,845
Σy = sum of all Y values = 589
Σx1y = sum of all (x1 * Y) = 232,988
Σx1^2 = sum of all (x1^2) = 80,037
Σx2^2 = sum of all (x2^2) = 46,693
Using the formula:
b1 = (n * Σx1y - Σx1 * Σy) / (n * Σx1^2 - Σx1^2)
= (11 * 232,988 - 2,577 * 589) / (11 * 80,037 - 2,577^2)
= (2,562,868 - 1,517,073) / (880,407 - 6,646,529)
= 1,045,795 / -5,766,122
= -0.181
Next, let's calculate the y-intercept (b0) of the regression line:
b0 = (Σy - b1 * Σx1) / n
= (589 - (-0.181) * 2,577) / 11
= (589 + 466.537) / 11
= 1,055.537 / 11
= 95.959
Now we have the slope (b1 = -0.181) and the y-intercept (b0 = 95.959).
The fitted line regression equation is:
y = 95.959 - 0.181x