Question

error analysis describe and correct the error in interpreting the graphing calculator display. linreg y=ax+b a≈-4.47 b≈23.16 r²≈.9989451055 r≈-.9994726136 the data have a strong positive correlation. the data do not have a strong positive correlation. the data have a weak negative correlation. the data do not have a strong positive correlation. the data have a weak positive correlation. the data do not have a strong positive correlation. the data have a strong negative correlation. the data do not have a strong positive correlation. the data do not have any correlation.

Explanation:

Step1: Analyze the correlation coefficient (r)

The correlation coefficient \( r \approx -0.99947 \). The sign of \( r \) indicates the direction of correlation (negative here), and the magnitude (close to -1) indicates a strong correlation.

Step2: Evaluate the original statement and options

The original statement claims a strong positive correlation, but \( r \) is negative and close to -1, so it's a strong negative correlation. We check the options:

• First option: "weak negative" is wrong (magnitude is strong).
• Second option: "weak positive" is wrong (sign and magnitude).
• Third option: "strong negative" matches \( r \approx -0.99947 \) (strong, negative).
• Fourth option: "no correlation" is wrong (r is close to -1, so there is strong correlation).

Answer:

The data do not have a strong positive correlation. The data have a strong negative correlation. (Corresponding to the third option among the given choices, e.g., if the third option is labeled as C, then C. The data do not have a strong positive correlation. The data have a strong negative correlation.)