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Practice Regression Lines and Bivariate Statistics Review In the questions in this Assignment you'll do a regressional analysis and describe the relationship (if any) between the explanatory and response variables. While the computations should be straightforward using the TI-83, think carefully about how to interpret these values in the context of the question. For example, if you were examining the linear relationship between age and income, remember to interpret the regression coefficient in terms of the amount of change in income associated with a one-year increase in age. Interpret the coefficient of determination (?) in terms of the percentage of variation in income that's explained by changes in age. In some instances you'll also predict values of the response variable using the least- squares regression line. If you recall, this simply involves substituting values into the regression equation and computing the predicted values. Also think about whether your predictions are examples of interpolation or extrapolation and the concerns that may arise with either type of prediction. Questions 1. The following table contains information about the robbery rate (number of robberies per 100,000 population) and percentage of urban population (percentage of people living in urban as opposed to rural areas) across a set of states: State Percentage of Robberies per Urban Population 100,000 People Massachusetts 91 193 Wisconsin 67 73 South Dakota 28 16 Virginia 72 106 South Carolina 60 99 Texas 81 240 Arizona 75 169 California 96 343 Arkansas 44 88 Hawaii 77 106 Source: Statistical Abstracts of the United States, 1988 Conduct a full regressional analysis using robbery rate as the response variable: A. Sketch the scatterplot with the least-squares line, and sketch the residual plot. Interpret your sketch. Remember, use robbery rate as the response variable, since that's the value you're trying to predict. (1 point) B. Write and interpret the correlation coefficient. (.5 points) C. Write the regression equation and interpret the regression coefficient. (1 point) D. Show and interpret the coefficient of determination. (.5 points) E. State whether you think there is a relationship between the two variables, and justify your answer. (1 point) F. We know that the percentage of urban population in Idaho is 35%. We also know that the percentage of urban population in Florida is 78%. Predict the robbery rates in each of these states. Are these extrapolations or interpolation, and are they valid predictions? (1 point)
