Question

Given the following set of data for a trivariate distribution
Y 6 10 9 14 7 5
X1 1 3 2 -2 3 6
X2 3 -1 4 7 2 -4
(i) Calculate the Multiple regression of Y on X1 and X2
(ii) Predict Y when X1=-1 and X2=4

Answer 1

Answer on Question #45836 – Math – Statistics and Probability

Given the following set of data for a trivariate distribution

Y 6 10 9 14 7 5

X1 1 3 2 -2 3 6

X2 3 -1 4 7 2 -4

(i) Calculate the Multiple regression of Y on X1 and X2

(ii) Predict Y when X1=-1 and X2=4

Solution

(i) To obtain the coefficients of regression equation $y = a + b_{1}x_{1} + b_{2}x_{2}$

we use the Method of Least Squares

(https://www.easycalculation.com/statistics/multiple-regression.php)

$$y(x_{1}, x_{2}) = 12.4247 - 1.48745x_{1} - 0.382845x_{2}$$

(ii) $y(-1,4) = 12.4247 - 1.48745 * (-1) - 0.382845 * 4 = 12.38077$

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