Clearly showed how yield Y depends on fertilizer x_1 alone, that is, it removed

Question

Clearly showed how yield Y depends on fertilizer x_1 alone, that is, it removed the bias of the confounding variable x_2. Multiple regression can give us answers to other interesting questions, too, for example: If irrigation were being considered, it would be important to know how Y depends on rainfall X_2 alone (without being founded with x_1) To answer this, look at Figure 13-2 where fertilizer X_1 is now constant, say at X_1= 400. If X_2 were to change from 10 to 30 inches, how much would yield increase? For each inch of rain fall, what is the estimated increase in yield? Forecasting is another important function of multiple regression. For example, use Figure 13-2 to predict the yield from a plot getting 300 pounds of fertilizer and 30 inches of rainfall. We have shown graphically how to eliminate the confounding effect of one variable, rainfall. What about the others-temperature, soil fertility, cultivation, and so on?

Explanation / Answer

a) Keeping X1 constant at 400, yield is 55 for x2 = 10 and yield is 70 for x2 = 30. slope = (70-55)/(30-10) = 0.75 increase in yield for every inch increase in rainfall.

b) Find the equation, slope = (80-70)/(700-400) = 10/300 = 1/30, 80 = 1/30*700 + b, b = 170/3

For x1 = 300, y = 1/30*300 + 170/3 = 66.67

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