Question 1

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 ?

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.

Question 2

In a multiple regression model y' = -11 + 4x₁ + 11x₂ + 7x₃ + 3x₄, if the value of x₂ increases by 2 and the value of x₃ decreases by 5, then the predicted value for y will

Accepted Answer

If x₂ increases by 2 and x₃ decreases by 5, then the new coefficients will be 11+2=13 for x₂ and 7-5=2 for x₃. Plugging these new coefficients into the original equation: y' = -11 + 4x₁ + 13x₂ + 2x₃ + 3x₄ Now we can see that the coefficient for x₃ has decreased by 5, which means that its effect on y will also decrease. Thus, the predicted value for y will decrease by 2*(-5) = -10. Therefore, the answer is (C) decrease by 13.

Question 3

If there are three independent variables x₁, x₂, and x₃ available, then the value of R² for a multiple regression of y using x₁, x₂, and x₃will always be smaller than the value of r² for a multiple regression of y using just x₁.

Accepted Answer

We cannot determine whether the value of R² will be smaller or larger without additional information about the relationships between the independent variables and the dependent variable.

Quiz 10: Correlation and Regression

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 ?

In a multiple regression model y' = -11 + 4x1 + 11x2 + 7x3 + 3x4, if the value of x2 increases by 2 and the value of x3 decreases by 5, then the predicted value for y will

If there are three independent variables x1, x2, and x3 available, then the value of R2 for a multiple regression of y using x1, x2, and x3 will always be smaller than the value of r2 for a multiple regression of y using just x1.

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 ?

In a multiple regression model y' = -11 + 4x₁ + 11x₂ + 7x₃ + 3x₄, if the value of x₂ increases by 2 and the value of x₃ decreases by 5, then the predicted value for y will

If there are three independent variables x₁, x₂, and x₃ available, then the value of R² for a multiple regression of y using x₁, x₂, and x₃will always be smaller than the value of r² for a multiple regression of y using just x₁.