"In Exercises 27 and 28, use the multiple regression equation ...

Question

"In Exercises 27 and 28, use the multiple regression equation to predict the y-values for the values of the independent variables.

28. Use the regression equation found in Exercise 25.

a. x_1 = 9.0, x_2 = 0.70

b. x_1 = 3.0, x_2 = 0.25

c. x_1 = 8.0, x_2 = 0.60

d. x_1 = 5.2, x_2 = 0.46"

Accepted Answer

Hello there. Today we're going to solve the following practice problem together. So first off, let us read the problem and highlight all the key pieces of information that we need to use in order to solve this problem. A multiple regression model is Y is equal to 5.0 plus 0.9 multiplied by X subscript 1 plus 1.2 multiplied by X subscript 2. What is the predicted value of Y when X subscript 1 is equal to 7.0 and X subscript 2 is equal to 3.0? Awesome. So it appears for this particular problem, based on all the information that's provided to us, we're asked to predict the value of Y when X subscript 1 is equal to 7.0 and X subscript 2 is going to be equal to 3.0. And to keep things simple, I'll just call it instead of saying X subscript 1 or X subscript 2, I'll just say X1 and X2. So with that in mind, now that we know that we're ultimately trying to determine this predicted value of Y, that's our final answer we're ultimately trying to solve for, let's read off our multiple choice answers to see what our final answer might be. A is 8.9, B is 18.4, C is 15.7, and D is 14.9. Awesome. Our first step that we need to take is we need to note that we're told that X1 is equal to 7.0, and we're told that X2 is equal to 3.0. And we need to substitute these two values into our equation that is given to us, which we're told that Y hat is equal to 5.0 plus 0.9 multiplied by X subscript 1 plus 1.2, so 1.2 multiplied by X2. So all we need to do is plug in our known variables, since we're told what X1 and X2 is, we can say that Y hat, which Y hat at this point is representing our predicted value for Y, and this is equal to 5.0 plus 0.9 multiplied by 7.0, because that's our value for X1. Plus 1.2 multiplied by, so 1.2 multiplied by our value of X2, which is 3.0. So we will determine that Y hat. Or if you want to, you could write it without the hat symbol if you want, we're asking to solve for the predicted value of Y and why in this case is predicted value of Y, where you can keep the hat, it doesn't really matter, but this value, which is the predicted value of Y, which we're ultimately trying to solve for when we plug in this expression into our calculator, once again taking 5.0 plus. 0.9 multiplied by 7.0 plus 1.2 multiplied by 3.0. When we plug in that expression into our calculator, we will find that it's simply equal to 14.9 when we round to one decimal place, and that is our final answer. Hooray, we did it, and this corresponds to multiple choice answer letter D, which is once again 14.9. Thank you so much for watching. Hopefully that helped, and I can't wait to see you in the next video. Bye.

"In Exercises 27 and 28, use the multiple regression equation to predict the y-values for the values of the independent variables.28. Use the regression equation found in Exercise 25.a. x_1 = 9.0, x_2 = 0.70b. x_1 = 3.0, x_2 = 0.25c. x_1 = 8.0, x_2 = 0.60d. x_1 = 5.2, x_2 = 0.46"

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"In Exercises 27 and 28, use the multiple regression equation to predict the y-values for the values of the independent variables.
28. Use the regression equation found in Exercise 25.
a. x_1 = 9.0, x_2 = 0.70
b. x_1 = 3.0, x_2 = 0.25
c. x_1 = 8.0, x_2 = 0.60
d. x_1 = 5.2, x_2 = 0.46"