Question

select the correct answer.

the 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.

he 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).

could this line of best fit be used to make reliable predictions?

no, because the slope of the line is closer to 0 than to 1, which indicates a weak association between the variables.
no, because the correlation coefficient is closer to 1 than to 0, which indicates a weak association between the variables.
yes, because the slope of the line is closer to 0 than to 1, which indicates a strong association between the variables.
yes, because the correlation coefficient is closer to 1 than to 0, which indicates a strong association between the variables.

Explanation:

Identify the correlation coefficient and its strength

$$ r = 0.948 $$

Since \(r = 0.948\) is very close to \(1\), it indicates a strong positive linear association between the variables.

Evaluate reliability of predictions

A correlation coefficient close to \(1\) means the data points lie close to the line of best fit, making the line highly reliable for predictions within the domain of the data.

Match with the correct option

The correct option must state "Yes" because the correlation coefficient (not the slope) is close to \(1\), indicating a strong association.

Answer:

• No, because the slope of the line is closer to 0 than to 1, which indicates a weak association between the variables.
• No, because the correlation coefficient is closer to 1 than to 0, which indicates a weak association between the variables.
• Yes, because the slope of the line is closer to 0 than to 1, which indicates a strong association between the variables.
• Yes, because the correlation coefficient is closer to 1 than to 0, which indicates a strong association between the variables. (Correct answer)