Insurance Premiums ~ Mona is interested in the relationship between the amount insurance companies pay out for automobile collision claims and what they charge their customers in insurance premiums. Using data from 2014, she selects a random sample of 20 US states. For each state, she calculates the losses incurred by insurance companies per insured driver (Losses) and the average insurance premium for drivers (Premiums). The scatter plot and a summary of the data is given below. The correlation between Losses and Premiums was found to be r = 0.6065. Round all calculated answers to 4 decimal places.
VariablesMeanSample SD
Losses134.742525.9635
Premiums895.132171.8535
1. The relationship between Losses and Premiums is best described as ? (Positive/Negative) and ? (Linear/Nonlinear) .
2. Calculate the slope and intercept for the linear regression equation that predicts Premiums from Losses. Note: Do not use rounded values for intermediate calculations!
Slope:
Intercept:
3. What is the R^2 for this study’s linear regression model of Premiums from Losses?
4. Lisa is evaluating Mona’s work and discovers that her home state was not included in Mona’s sample. Lisa calculates the losses per insured driver for her state to be $254.78. Is it appropriate for Lisa to use Mona’s regression equation to estimate the insurance premium for her state?
(Yes/No) because
A. Lisa's value for Losses is within the range of the data Mona used to create the model.
B. Regression equations cannot be used to make predictions.
C. Mona's model is only valid for the states she used to create the model.
D. Lisa's value for Losses is not within the range of the data Mona used to create the model.
5. Lisa also decides to examine the residuals for Mona’s model to determine if the conditions for linear regression have been met. Which condition is Lisa checking with the following plot?
A. Lisa is checking to see if the residuals are nearly normal.
B. Lisa is checking to see if the data show a linear trend.
C. Lisa is checking to see if the variability of points around the least squares line is roughly constant.