Suppose a multiple regression model given by y259x1946x22299

Suppose a multiple regression model given by y^=2.59x_1+9.46x_2+22.99. What would an interpretation of the coefficient of x_1 be? Fill in the blank below.

An interpretation of the coefficient of x_1 would be, \"if x_1 decreases by 1 unit, then the response variable will decrease by ___ units, on average, while holding x_2 constant.\"

Solution

y^=2.59x_1+9.46x_2+22.99

here the variable is Y

and it clearly depends in X1 AND X2

we have keep the X2 as constant and as per the regression line the x1 is directly proportional to Y hence if we reduce the X1 by 1 unit the variable will decrease by 2.59 units (1*2.59 = 2.59).

hence the answer will be 2.59