Table 8.2
The Agricultural Extension Agent's Office has tracked fertilizer application and crop yields for a variety of chickpea and has recorded the data shown in the following table. Their staff statistician developed the regression model and computed the performance statistics displayed below the data.

-Use the information in Table 8.2. If the correlation coefficient were negative, which of these statements would be True?
A) The coefficient of determination would also be negative.
B) An increase in fertilizer would result in a decrease in crop yield.
C) Applying no fertilizer would mean a negative crop yield.
D) The standard error would also be negative.

Question

Table 8.2
The Agricultural Extension Agent's Office has tracked fertilizer application and crop yields for a variety of chickpea and has recorded the data shown in the following table. Their staff statistician developed the regression model and computed the performance statistics displayed below the data.
 
-Use the information in Table 8.2. If the correlation coefficient were negative, which of these statements would be True?
A) The coefficient of determination would also be negative. 
B) An increase in fertilizer would result in a decrease in crop yield. 
C) Applying no fertilizer would mean a negative crop yield. 
D) The standard error would also be negative.

Quizplus · Accepted Answer

A negative correlation coefficient means that an increase in fertilizer would result in a decrease in crop yield. The coefficient of determination would still be positive, as it represents the proportion of variation in crop yield that can be explained by fertilizer application. Applying no fertilizer would not necessarily mean a negative crop yield, as the model does not account for other factors that can affect crop yield. The standard error can never be negative.

Table 8.2 the Agricultural Extension Agent's Office Has Tracked Fertilizer Application and Application