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# Data Least Squares Regression Calculation

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For a set of data, the total variation or sum of squares for y is SST - 143.0 and the error sum of squares is SSE = 24.0. What proportion of the variation in y is explained by the regression equation?

2. A. Determine the least squares regression line and calculate r.

B. What proportion of the variability in steel shipments for motor vehicles is explained by the regression equation?

C. During the year in which US production of motor vehicles is 12.0 million, what would be the prediction for the number of tons of domestic steel used for vehicle prodution?

Year x = US Production y = tons of
of motor vehicles domestic steel
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2000 12.83 million 16.06 million
2001 11.52 14.06
2002 12.33 14.00
2003 12.15 15.88
2004 12.02 13.86

Using the regression line developed:
D. Use the 0.05 level in testing whether the population coefficient of correlation could be zero.
E. Use the 0.05 level in testing whether the population regressin equation could have a slope of zero.
F. Construct the 95% confidence interval for the slope of the population regression equation.