"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.

4. Sorghum Yield The equation used to predict the annual sorghum yield (in bushels per

acre) is y = 80.1-20.2x_1 +21.2x_2

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

a. x_1 = 5.5, x_2 = 3.9

b. x_1 = 8.3, x_2 = 7.3

c. x_1 = 6.5, x_2 = 5.7

d. x_1 = 9.4, x_2= 7.8"

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 multiple regression model for predicting annual wheat output in units of tons is Y is equal to 8900 plus 5.102 multiplied by X 1 minus 3.876 multiplied by X subscript 2, where X subscript 1 is the number of acres sown. And X subscript 2 is the number of acres harvested. Estimate the output if X subscript 1 is equal to 25,000 and X subscript 2 is equal to 24,300. OK, so it appears for this particular prompt, we're asked to estimate what the output value would be given a specific value for X subscript 1 and X subscript 2, and based on all the other information that is provided to us by the prom itself. So now that we know that we're ultimately trying to solve for this output value, let us read off our multiple choice answers to see what our final answer might be. A is 18,234.8. B is 17,990.4, C is 42,263.2, and D is 19,785.6. OK, so our first step that we need to take in order to solve this particular problem is we need to substitute in our known variables into our given equation for the regression equation. So we're told that X subscript 1 is equal to 25,000, and we're also told that X subscript 2, or we can say X1 and X2, we're told that X2 is equal to 24,300. And when we plug in our known variables into our equation, we will find that Y hat is equal to 8900 plus 5.102 multiplied by our value of Exxon, which was 25,000. And then we need to subtract 3.876 multiplied by our value of X2, which is 24,300. And when we plug in this expression into our calculator, we will find that Y hat is equal to 42,263.2 when me round to one decimal place, and that's it. That's our final answer. So this problem is very easy to solve for. You just need to understand what the problem's asking us to do. So essentially this problem is just asking us to solve for the output. And in order to solve for the output, we need to plug in our values that are given to us, which is X1 and X2, into our provided equation to solve for what the ultimate like that what will be the ultimate outcome, which is why we're trying to solve for why, and that's what we did, and that's it. So looking at our multiple choice answers, the correct answer without a doubt will have to be multiple choice answer letter C, which once again is 42,263.2. 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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