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A family would like to build a linear regression equation to predict the amount of grain harvested per acre of land on their farm. They subdivide their land into several smaller plots of land for testing and would like to select an explanatory variable they can control. Which of the following is an appropriate explanatory variable that the family could use to create a linear regression equation?

a. The total amount of rainfall recorded at their farm ).
b. The type of crop planted in the plot the previous year.
c. The average daily temperature at their farm.
d. The variety of grain planted in the plot.
e. The amount of fertilizer applied to each plot of land.

Answer :

Answer:

The correct option is;

The amount of fertilizer applied to each plot of land

Step-by-step explanation:

The value which the family would like to predict = The amount of grain harvested per acre of land on their farm

The methodology to be used for the prediction = Linear regression equation

The general form of a linear regression equation is Y = a + b·X

Where;

X = The independent or explanatory variable

Y = The dependent variable

b = The gradient or slope which is the rate of change

a = The y-intercept, the initial value of the dependent variable at the start of observation when the explanatory variable is 0

Therefore, given that the family would like to predict the amount of grain produced per acre, we have;

The variable which is whose value depends on other variable is the variable to be predicted and it is the same as the dependent variable

Therefore, the dependent variable is to be predicted, which gives;

The amount of grain produced per acre which is the dependent variable is to be predicted

Hence, Y = The amount of grain produced per acre

The explanatory variable or the independent variable is the variable which determines the value and in which the dependent variable depends as such it can be used to explain the values of the amount of grain growing per acre, therefore, we have;

The explanatory variable can be the amount of fertilizer applied to each plot of land

Therefore;

X = The amount of fertilizer applied to each plot of land

Therefore, we have;

The amount of grain produced per acre = The initial growth of grain per acre + (Rate of change of grains produced per unit of fertilizer added) × (The amount of fertilizer applied to each plot of land).

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The explanatory variable refers to the independent variable in an experiment which is used to tweak the value of the measured variable. An appropriate explanatory variable would be the amount of fertilizer applied to each plot of land

  • Explanatory would be one which has a reasonable degree of correlation or relationship with the measured variable.

  • Since, we'll like to measure the output on each plot using the amount of grain harvested, then a factor which closely affects the level of crop yield should be selected.

  • The amount of Rainfall and temperature are close factors, however, they cannot be controlled.

  • The most appropriate and highly correlated explanatory variable would be the amount of fertilizer applied to each plot of land.

Therefore, the amount of fertilizer is a good factor to measure the yield or amount of grain harvested on each plot.

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