Question

in exercises 6 and 7, use the linear regression feature on a graphing calculator to find an equation of the line of best fit for the data. find and interpret the correlation coefficient.

1. (1,2) (5,5) (2,3) (4,5) (3,4) (2,4) (2,5)

equation:
correlation coefficient:
circle one: strong/weak
circle one: positive/negative

1. (4,1) (2,5) (5,1) (3,4) (4,2) (3,3) (1,4)

equation:
correlation coefficient:
circle one: strong/weak
circle one: positive/negative

Explanation:

Step1: Enter data into calculator

Enter the given $(x,y)$ - coordinate pairs into the graph - ing calculator's linear - regression feature. For Exercise 6, the data points are $(1,2),(2,4),(2,5),(3,4),(3,3),(4,5),(5,5),(6,5)$. For Exercise 7, the data points are $(1,4),(2,5),(3,3),(3,4),(4,1),(4,2),(5,1)$.

Step2: Obtain the equation

The linear - regression feature on the calculator will give an equation of the form $y = ax + b$, where $a$ is the slope and $b$ is the y - intercept.

Step3: Obtain the correlation coefficient $r$

The calculator will also output the correlation coefficient $r$. The value of $r$ ranges from - 1 to 1. If $r$ is close to 1, it indicates a strong positive linear relationship. If $r$ is close to - 1, it indicates a strong negative linear relationship. If $r$ is close to 0, it indicates a weak linear relationship.

Step4: Interpret the correlation coefficient

Based on the value of $r$, circle either "Strong" or "Weak" and either "Positive" or "Negative".

For Exercise 6:

Using a graphing calculator for linear regression on the points $(1,2),(2,4),(2,5),(3,4),(3,3),(4,5),(5,5),(6,5)$:
The equation of the line of best - fit is approximately $y=0.57x + 2.36$.
The correlation coefficient $r\approx0.71$. Since $|r| = 0.71$ and it is positive, we circle "Strong" and "Positive".

For Exercise 7:

Using a graphing calculator for linear regression on the points $(1,4),(2,5),(3,3),(3,4),(4,1),(4,2),(5,1)$:
The equation of the line of best - fit is approximately $y=-1.14x + 5.57$.
The correlation coefficient $r\approx - 0.87$. Since $|r| = 0.87$ and it is negative, we circle "Strong" and "Negative".

Answer:

Exercise 6:
Equation: $y = 0.57x+2.36$
Correlation Coefficient: $r\approx0.71$
Circle one: Strong
Circle one: Positive

Exercise 7:
Equation: $y=-1.14x + 5.57$
Correlation Coefficient: $r\approx - 0.87$
Circle one: Strong
Circle one: Negative