Question

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

Answer 1

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