Solve the following problem:
The U.S Department of Transportation and Safety performed an analysis to determine safe driving speeds. To obtain information about the safe driving speed, it analyzed data from multiple countries comparing the maximum allowed speed limit to the observed death rate. The analysis revealed the following:
Refer to the Minitab output below to answer questions A through G.
Regression Equation
Death rate (per 100 million vehicles = -0.535979 + 0.0789418 Speed limit (miles per hour)
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Coefficients
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Term
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Coef
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SE Coef
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T
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P
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95% CI
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Constant
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-0.535979
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2.34352
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-0.22871
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0.825
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(-5.94014, 4.86818)
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Speed limit (miles per hour)
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0.078942
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0.03849
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2.05106
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0.074
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(-0.00981, 016770)
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Summary of Model
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S = 0.836621
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R-Sq = 34.46%
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R-Sq(adj) = 26.27%
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PRESS = 10.8252
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R-Sq(pred) = -26.70%
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Analysis of Variance
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Source
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DF
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Seq SS
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Adj SS
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Adj MS
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F
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Regression
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1
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2.94453
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2.94453
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2.94453
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4.20687
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Speed limit (miles per hour)
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1
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2.94453
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2.94453
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2.94453
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4.20687
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Error
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8
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5.59947
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5.59947
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0.69993
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Lack-of-Fit
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3
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3.37947
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3.37947
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1.12649
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2.53714
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Pure Error
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5
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2.22000
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2.22000
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0.44400
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Total
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9
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8.54400
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Source
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P
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Regression
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0.074385
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Speed limit (miles per hour)
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0.074385
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Error
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Lack-of-Fit
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0.170419
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Pure Error
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Total
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Predicted Values for New Observations
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New Obs
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Fit
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SE Fit
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95% CI
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95% PI
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1
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4.20053
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0.265262
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(3.58883, 4.81222)
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(2.17663, 6.22443)
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Values of Predictors for New Observations
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New Obs
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Speed limit (miles per hour)
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1
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60
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(A) Analyze the above output to determine the regression equation.
(B) What conclusions are possible using the meaning of b0 (intercept) and b1 (regression coefficient) in this problem? (That is, explain the meaning of the coefficients.)
(C) What conclusions are possible using the coefficient of determination (r-squared)?
(D) Calculate the coefficient of correlation. Interpret this value.
(E) Does this data provide significant evidence (a=0.05) that the death rate is associated with the speed limit? Find the p-value and interpret.
(F) Determine the average death rate for a speed limit of 60 miles per hour.
(G) What is the 95% confidence interval for the death rate for a speed limit of 60 miles per hour? What conclusion is possible using this interval?