Algebra 1 Lesson 3-5 and 3-6 Classwork

11 of 13 11 of 13 Items

Question
POSSIBLE POINTS: 7.14
Use a graphing calculator to find the equation of the line of best fit for the data. Find the value of the correlation coefficient r. Predict the missing value in the table.

Responses

y = 2.964x + 62.286, r = 0.991; about 99%
y = 2.964 x + 62.286 , r = 0.991; about 99%

y = 2.964x + 62.286, r = 0.991; about 89%
y = 2.964 x + 62.286 , r = 0.991; about 89%

y = 62.286x + 2.964 , r = 0.991; about 95%

y = 62.286 x + 2.964 , r = 0.991; about 95%

y = 3x + 65, r = 0.951; about 92%

1 answer

To determine the correct answer regarding the equation of the line of best fit and the correlation coefficient \( r \), we need to analyze the provided options.

  1. Equation Format: The general format for a linear equation is \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept.
  2. Correlation Coefficient: The correlation coefficient \( r \) ranges from -1 to 1, where values close to 1 (like 0.991) indicate a strong positive correlation, and values closer to 0 indicate no correlation.

Given your options, the most plausible candidates based on high correlation and proper format are:

  • Option 1: \( y = 2.964x + 62.286, r = 0.991; \) about 99%
  • Option 2: \( y = 2.964x + 62.286, r = 0.991; \) about 89%
  • Option 3: \( y = 62.286x + 2.964, r = 0.991; \) about 95%
  • Option 4: \( y = 62.286x + 2.964, r = 0.991; \) about 95%
  • Option 5: \( y = 3x + 65, r = 0.951; \) about 92%

Analyzing the Options:

  • Options 1 and 2 have the same equation, but they differ in the percentage (99% vs. 89%).
  • Options 3 and 4 have the equation in the incorrect format (the coefficients and variables are reversed).
  • Option 5 offers a different slope and y-intercept with a slightly lower correlation value, indicating a weaker correlation.

Since options 1 and 2 are consistent with each other, and given the correlation coefficient \( r = 0.991 \) is very high, it is likely a strong relationship. Between the two:

  • If the correct correlation coefficient is as stated, then Option 1 (with a 99% prediction accuracy) is more reliable than Option 2 (which states 89%).

Conclusion:

The correct response is:

y = 2.964x + 62.286, r = 0.991; about 99%.