Question

"Predicting y-Values In Exercises 3-6, use the multiple regression equation to predict the y-values for the values of the independent variables.
6. Elephant Weight The equation used to predict the weight of an elephant (in kilograms) is
y =- 4016+11.5x_1+7.55x_2+12.5x_3
where x_1 represents the girth of the elephant (in centimeters), x_2 represents the length of the elephant (in centimeters), and x_3 represents the circumference of a footpad (in
centimeters). (Source: Field Trip Earth)
a. x_1 = 421, x_2 = 224, x_3 = 144
b. x_1 = 311, x_2 = 171, x_3 = 102
c. x_1 = 376, x_2 = 226, x_3 = 124
d. x_1 =231, x_2 = 135, x_3 = 86"

Accepted Answer

Identify the multiple regression equation given: y = -4016 + 11.5 $$x_1 + 7.55$$ $$x_2 + 12.5$$ $$x_3$$, where $$x_1$$, $$x_2$$, and $$x_3$$ are the independent variables representing girth, length, and footpad circumference respectively. For each set of values of $$x_1$$, $$x_2$$, and $$x_3$$, substitute these values into the regression equation. For example, for part (a), substitute 421 for $$x_1$$, 224 for $$x_2$$, and 144 for $$x_3. $$Calculate the products of each coefficient with its corresponding variable: multiply 11.5 by $$x_1$$, 7.55 by $$x_2$$, and 12.5 by $$x_3. $$Add the results from the multiplications together along with the constant term -4016 to find the predicted value of y for each set of independent variables. Repeat steps 2 to 4 for each of the remaining sets of values (b, c, and d) to find the predicted elephant weights for all given measurements.

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