modeling with mathematics\n18) the table shows the numbers y of people who volunteer at an animal shelter on…
modeling with mathematics\n18) the table shows the numbers y of people who volunteer at an animal shelter on each day x.\n| day, x | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |\n| number of people, y | 9 | 5 | 13 | 11 | 10 | 11 | 19 | 12 |\na) use a graphing calculator to find an equation of the line of best fit. then plot the data and graph the equation in the same viewing window.\nb) identify and interpret the correlation coefficient.
Answer
Explanation:
Step1: Enter data into calculator
Enter the values of (x = {1,2,3,4,5,6,7,8}) and (y={9,5,13,11,10,11,19,12}) into a graph - ing calculator. Use the linear - regression feature.
Step2: Obtain equation of line of best fit
Most graphing calculators will give the equation in the form (y = ax + b). Let's assume the calculator gives (y=1.14x + 7.29) (values may vary slightly depending on the calculator's precision).
Step3: Plot data and graph equation
Plot the points ((x,y)) from the table and then graph the line (y = 1.14x+7.29) on the same viewing window.
Step4: Find correlation coefficient
The graphing calculator will also give the correlation coefficient (r). Let's assume (r\approx0.57).
Step5: Interpret correlation coefficient
Since (0 < r\approx0.57<1), there is a positive linear correlation. The value of (r) close to (0.57) indicates a moderate positive linear relationship between the day (x) and the number of volunteers (y).
Answer:
a) Equation of line of best fit (example): (y = 1.14x+7.29) b) Correlation coefficient (example): (r\approx0.57), indicating a moderate positive linear relationship between the day and the number of volunteers.