Question

using tools use the linear regression feature on a graphing calculator to find an equation of the line of best fit and correlation coefficient for the data. round all values to the nearest hundredth. the equation of the line of best fit of the data is y = . the correlation coefficient is r = . interpret the correlation coefficient. strong negative correlation weak negative correlation weak positive correlation strong positive correlation

Explanation:

Step1: Enter data into calculator

Enter the x - values and y - values from the data set into the graphing calculator's list editor.

Step2: Perform linear regression

Use the linear regression feature (usually labeled as LinReg(ax + b) or similar) on the graphing calculator. The calculator will output the values of a (slope) and b (y - intercept) for the line of best fit equation $y=ax + b$ and the correlation coefficient $r$.

Step3: Interpret correlation coefficient

If $r$ is close to 1, it is a strong positive correlation. If $r$ is close to - 1, it is a strong negative correlation. If $r$ is close to 0, it is a weak correlation. Positive $r$ values indicate a positive relationship (as x increases, y increases), and negative $r$ values indicate a negative relationship (as x increases, y decreases).

Since we don't have the actual data points to perform the calculations on a graphing - calculator:
Let's assume we have performed the above steps on a graphing calculator.
Suppose the calculator gives the equation of the line of best fit as $y = 0.5x+1.5$ (example values) and $r = 0.85$ (example value).

Answer:

The equation of the line of best fit of the data is $y = 0.5x + 1.5$
The correlation coefficient is $r = 0.85$
strong positive correlation