"Predicting y-Values In Exercises 3-6, use the multiple regres...

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.

3. Cauliflower Yield The equation used to predict the annual cauliflower yield (in pounds

per acre) is y=24,791+4.508x_1-4.723x_2

where x_1 is the number of acres planted and x_2 is the number of acres harvested.(Adapted from United States Department of Agriculture)

a. x_1 = 36,500, x_2 = 36,100

b. x_1 = 38,100, x_2 = 37,800

c. x_1 = 39,000, x_2 = 38,800

d. x_1 = 42,200, x_2 = 42,100"

Accepted Answer

Hello there. Today we're gonna 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 researcher uses the regression equation Y equals 15,320 plus 3.215 multiplied by X 1 minus 2.987 multiplied by X subscript 2 to predict the annual tomato yield in units of pounds per acre. Where X subscript 1 is the number of acres fertilized and X subscript 2 is the number of acres irrigated, what is the predicted yield when X subscript 1 is equal to 12,500 and X subscript 2 is equal to 11,900? Awesome. So it appears for this particular problem, we're asked to take all the information that is provided to us by the prom itself, and we're asked to determine what is the predicted yield of tomatoes per acre when X subscript 1 equals a specific value and X subscript 2 equals a specific value. So now that we know that we're ultimately trying to determine the predicted yield value for this particular problem, let's read off our multiple choice answers to see what our final answer might be. A is 18,500.7, B is 19,962.2, C is 17,950.3, and D is 19,782.5. Awesome. So our first step that we need to take in order to solve for this particular problem is we need to substitute the value X subscript 1 or X1 is equal to 12,500 and X2 X subscript 2 is equal to 11,900, and we need to plug our value for X1 and X2 into our regression equation. And you will find that Y hat is equal to 15,320 plus 3.215 multiplied by 12,500. Minus 2.987 multiplied by our value for X2, which is 11,900. And we will find when we plug this into our calculator, when we plug this expression into our calculator, we will find. That Y hat is equal to 19,962.2 when we round. To one decimal place. Now once again, this is all all we need to do for this problem. It's very simple, is we just need to be able to recognize that we're trying to find the predicted yield. So in order to find the predicted yield, we have to take our values that are provided to us which we're given the values for X1 and X2, we need to plug it back into our equation that is given to us for the problem itself to determine what the predicted yield will be. And it's determined by the specific values of X1 and X2 when we plug it into the equation itself. And that's it. We've officially solved for this problem, very simple problem. You just need to understand what the problem's asking you to do. That's the hardest part. And looking at our multiple choice answers, the correct answer without a doubt has to be multiple choice answer letter B, which once again is 19,962.2. And that's it. Thank you so much for watching. Hopefully that helped and I can't wait to see you in the next video. Bye.

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