select the correct answer.\nthe developer of a new plant fertilizer gathered data about the quantity of…

select the correct answer.\nthe developer of a new plant fertilizer gathered data about the quantity of fertilizer applied to a lemon tree and the number of lemons it produced. he used a graphing tool to organize the data in a scatter - plot and find the line of best fit.\nhe found that the relationship between grams of fertilizer, x, and the number of lemons, y, is modeled by the equation y = 0.316x + 12.214, and the correlation coefficient for the data is 0.948.\ncould this line of best fit be used to make reliable predictions?\na. no, because the slope of the line is closer to 0 than to 1, which indicates a weak association between the variables.\nb. no, because the correlation coefficient is closer to 1 than to 0, which indicates a weak association between the variables.\nc. yes, because the slope of the line is closer to 0 than to 1, which indicates a strong association between the variables.\nd. yes, because the correlation coefficient is closer to 1 than to 0, which indicates a strong association between the variables.

select the correct answer.\nthe developer of a new plant fertilizer gathered data about the quantity of fertilizer applied to a lemon tree and the number of lemons it produced. he used a graphing tool to organize the data in a scatter - plot and find the line of best fit.\nhe found that the relationship between grams of fertilizer, x, and the number of lemons, y, is modeled by the equation y = 0.316x + 12.214, and the correlation coefficient for the data is 0.948.\ncould this line of best fit be used to make reliable predictions?\na. no, because the slope of the line is closer to 0 than to 1, which indicates a weak association between the variables.\nb. no, because the correlation coefficient is closer to 1 than to 0, which indicates a weak association between the variables.\nc. yes, because the slope of the line is closer to 0 than to 1, which indicates a strong association between the variables.\nd. yes, because the correlation coefficient is closer to 1 than to 0, which indicates a strong association between the variables.

Answer

Explanation:

Step1: Understand correlation coefficient concept

The correlation coefficient $r$ measures the strength and direction of a linear relationship between two variables. Values of $r$ range from - 1 to 1. A value close to 1 or - 1 indicates a strong linear relationship, and a value close to 0 indicates a weak linear relationship.

Step2: Analyze given correlation coefficient

The given correlation coefficient is $r = 0.948$, which is close to 1. This implies a strong positive - linear association between the grams of fertilizer ($x$) and the number of lemons ($y$).

Step3: Evaluate line of best - fit reliability

Since there is a strong linear association (as indicated by the correlation coefficient close to 1), the line of best - fit $y = 0.316x+12.214$ can be used to make reliable predictions.

Answer:

D. Yes, because the correlation coefficient is closer to 1 than to 0, which indicates a strong association between the variables.