10.1 Scatter Diagrams and Linear Correlation
Guided Practice 1: Merchandise loss due to shoplifting, damage, and other causes is called shrinkage. Shrinkage is a major concern to retailers. The managers of Terrapin Sportswear believe there is a relationship between shrinkage and number of clerks on duty. To explore this relationship, a random sample of 6 weeks was selected. During each week the staffing level of sales clerks was kept constant and the dollar value of the shrinkage was recorded.
Number of Sales Clerks / 12 / 11 / 15 / 9 / 13 / 8Shrinkage / 15 / 20 / 9 / 25 / 12 / 31
a) Create a scatter plot of the data on the TI-83
b) What is the value of r? Determine the type of correlation, if any.
Solution:
a) Scatter plot: Calculator Commands
b)
Exercise 1: In one of the Boston city parks, there has been a problem with muggings in the summer months. A police cadet took a random sample of 10 days (out of the 90-day summer) and compiled the following data. For each day, x represents the number of police officers on duty in the park and y represents the number of reported muggings on that day.
x / 10 / 15 / 16 / 1 / 4 / 6 / 18 / 12 / 7y / 5 / 2 / 1 / 9 / 7 / 8 / 1 / 5 / 6
a) Use the Stat Plot function to construct the plot. Enter the x-values into list L1 and the y-values into list L2. What can you conclude?
b) Use the TI-84 to calculate the correlation coefficient for the data. What can you conclude?
10.2 Linear Regression
Guided Practice 1: Merchandise loss due to shoplifting, damage, and other causes is called shrinkage. Shrinkage is a major concern to retailers. The managers of H.R. Merchandise believe there is a relationship between shrinkage and number of clerks on duty. To explore this relationship, a random sample of 6 weeks was selected. During each week the staffing level of sales clerks was kept constant and the dollar value of the shrinkage was recorded.
Number of Sales Clerks / 12 / 11 / 15 / 9 / 13 / 8Shrinkage / 15 / 20 / 9 / 25 / 12 / 31
a) Create a scatter plot and least-squares regression line on the TI-84
b) Predict the shrinkage when 10 clerks are on duty
LSRL Equation:
Predicted Shrinkage:
Exercise 1: Let’s find the least-squares equation relating the variables x=size of caribou population (in hundreds) and y =size of wolf population in Denali National Park. Use x as the explanatory variable and y as the response variable. A random sample gave the following data:
x / 30 / 34 / 27 / 25 / 17 / 23 / 20y / 66 / 79 / 70 / 60 / 48 / 55 / 60
a) Identify the explanatory and response variables
b) Make a scatter plot of the data
c) Find the linear regression line for the data
d) Interpret the slope of the line in this application
e) Predict the size of the wolf population when the caribou population is 2100
f) Identify the explanatory and response variables
g) Predict the size of the wolf population when the caribou population is 2100
Exercise 2: A large industrial plant has seven divisions that do the same type of work. A safety inspector visits each division of 20 workers quarterly. The number x of work-hours devoted to safety training and the number y of work-hours lost due to industry-related accidents are recorded for each separate division below.
Training / 10.0 / 19.5 / 30.0 / 45.0 / 50.0 / 65.0 / 80.0Hours / 80 / 65 / 68 / 55 / 35 / 10 / 12
a) Construct a scatter plot and find the equation of the LSRL
b) Identify the slope and y-intercept of the regression line and interpret each value in context
c) Create and interpret the residuals plot on the TI-84
Exercise 3: Find and interpret the residual for a plant that has received 40 hours of training and lost work 55 hours.
Exercise 4: Refer to the dataset from the previous exercise.
a) Use your calculator to compute r, r2,