Question

Using graphing software, create a scatter plot of the data. Predict the line of best fit, and sketch it on your graph. Next, answer these questions1. which variable did you plot of the x-axis, and which on the y-axis? why?2. Write equation of the line of best fit using the slop intercept formula. Show work3. What does the slope of the line represent within the context of your graph? what does the y-intercept represent?4. test the residuals of two other points to determine how well the line of best fit models the data5. use the line of best fit to help you describe the data correlation6. using the line of best fit that you found in question two, how tall is a person whose arm span is 66 inches?7. according to your line of best fit, what is the arm span of a 74-inch tall person?

Answer 1

Plotting the data set:

1.Plotting the x-axis as the arm span because this is the independent variable, and the height as y-axis because it's dependent variable.

2. Equation of a line is represented by:

`\begin{gathered} y=mx+b \\ m=\text{slope} \\ b=y-\text{intercept} \end{gathered}`

Line that best fits the data set is:

`y=x+1`

3. The slope represents the constant rate of change between two variables, so that means for 1 inch of arm span, the height increase 1 too.

4. Residual is the difference between the measured value and the predicted value of a regression model. To find the residual you must take the predicted value and subtract it from the measured value:

Measured value: 50

Predicted value: 47

Residual:

`50-47=3`

5. The variables are linearly related since they change together at a constant rate.

6. To calculate how tall is a person whose arm span is 66, substitute x=66

`\begin{gathered} y=66+1 \\ y=67\text{ inches} \end{gathered}`

A person whose arm span is 66 inches would be 67 inches tall.

7. To calculate what is the arm span of 74-inch tall person, we must substitute y=74 and solve for x:

`\begin{gathered} 74=x+1 \\ x=74-1 \\ x=73 \end{gathered}`

The arm span for a 74-inch tall person, would be 73 inches.