In examining per capita incomes for U S states over time one often finds that poor states tend to stay poor and wealthy states

Question

In examining per capita incomes for U S states over time one often finds that poor states tend to stay poor and wealthy states tend to stay wealthy So predictions about later years may sometimes be made from knowledge of previous years Consider the 1999 per capita income for a state denoted by y and its 1980 per capita income denoted by x The following bivariate data give the per capita income in thousands of dollars for a sample of fifteen states in the years 1980 and 1999 source U S Bureau of Economic Analysis Survey of Current Business May 2000 The data are plotted in the scatter plot in Figure 1 Colorado New Mexico Virginia New York Arizona Louisiana Hawail Michigan Arkansas Oregon Ohio Wisconsin Alabama Maine lowa Arkansas Oregon Ohio Wisconsin Alabama 1980 per capita 1999 per capita income x income y in 1000s in 1000s 10 8 8 4 10 2 11 1 9 6 8 8 11 5 10 4 7 6 10 2 10 1 10 2 7 9 8 4 9 7 Maine Lowa Send data to calculator 7 6 10 2 10 1 10 2 7 9 8 4 9 7 31 7 22 1 29 5 33 9 25 3 22 8 27 8 27 8 22 1 27 1 27 1 27 4 22 9 25 0 25 7 22 1 27 1 27 1 27 4 22 9 25 0 25 7 Send data to Excel woorde vad 6661 50001 Figure 1 34 32 1980 per capita income in 1000s Figure 1 20 1980 per capita income in 1000s a What is the value of the slope of the least squares regression line for these data Round your answer to at least two decimal places Expa ol b What is the value of the y intercept of the least squares regression line for these data Round your answer to at least two decimal places EB The value of the sample correlation coefficient r for these data is approximately 0 854 Answer the following Carry your intermediate computations to at least four decimal places and round your answers as specified below If necessa list of formulas 183

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