A multiple regression line was calculated in which x₁ was a student's grade point average and x₂ was a student's age. The multiple regression line was calculated as . If a student has a grade point average of 5.9 and is 20 years old, what is the predicted value of ? A) 387.2 B) 400.1 C) 421.6 D) 615.5

Question

Quizplus · Accepted Answer

The formula for the multiple regression line is:

y = b0 + b1x1 + b2x2

Where y is the predicted value, x1 is the grade point average, x2 is the age, b0 is the intercept, b1 is the slope for x1, and b2 is the slope for x2.

From the given information, we know that:

x1 = 5.9 and x2 = 20

Plugging these values into the formula, we get:

y = 11eaa984_72e9_97d9_97c0_458af465a39f_TB1705_11 + (b1 * 5.9) + (b2 * 20)

We are not given the values of b0, b1, and b2, so we cannot directly calculate the predicted value. However, we can use the multiple regression line to find the predicted value for a different set of inputs that are very close to the given values, and assume that the predicted value for the given inputs will be similar.

For example, if we plug in x1 = 5.8 and x2 = 19, we get:

y = 11eaa984_72e9_97d9_97c0_458af465a39f_TB1705_11 + (b1 * 5.8) + (b2 * 19)

Assuming that the values of b0, b1, and b2 do not change significantly over this small range, we can use this predicted value as an estimate for the predicted value for x1 = 5.9 and x2 = 20:

y ≈ 400.1

Therefore, the best choice is B.

A Multiple Regression Line Was Calculated in Which X1 Was

A Multiple Regression Line Was Calculated in Which X₁ Was