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An agricultural scientist planted alfalfa on several plots
Chapter 7, Problem 11E(choose chapter or problem)
An agricultural scientist planted alfalfa on several plots of land, identical except for the soil pH. Following are the dry matter yields (in pounds per acre) for each plot.
a. Construct a scatterplot of yield (y) versus pH (x). Verify that a linear model is appropriate.
b. Compute the least-squares line for predicting yield from pH.
c. Compute the fitted value and the residual for each point.
d. If the pH is increased by 0.1, by how much would you predict the yield to increase or decrease?
e. Predict the yield for a pH of 5.5.
f. Can the least-squares line be used to predict the yield for a pH of 7? If so, predict the yield. If not, explain why not.
g. For what pH would you predict a yield of 1500 pounds per acre?
Questions & Answers
QUESTION:
An agricultural scientist planted alfalfa on several plots of land, identical except for the soil pH. Following are the dry matter yields (in pounds per acre) for each plot.
a. Construct a scatterplot of yield (y) versus pH (x). Verify that a linear model is appropriate.
b. Compute the least-squares line for predicting yield from pH.
c. Compute the fitted value and the residual for each point.
d. If the pH is increased by 0.1, by how much would you predict the yield to increase or decrease?
e. Predict the yield for a pH of 5.5.
f. Can the least-squares line be used to predict the yield for a pH of 7? If so, predict the yield. If not, explain why not.
g. For what pH would you predict a yield of 1500 pounds per acre?
ANSWER:
Step 1 of 8
a.
To construct the scatterplot of the given data that is yield (y) vs pH (x);
The scatterplot is illustrated by plotting the pH values on the x-axis and yield on y-axis.
Since the data points are approximately linearly plotted, it can be said that there is almost a linear relationship between the variables.
Therefore, there is a positive linear relationship between pH values and yield.