The first column ( Speed ) is X, or the independent, variable and the second col
ID: 3051079 • Letter: T
Question
The first column (Speed) is X, or the independent, variable and the second column (Power) is Y, or the dependent, variable. Use MINITAB to obtain the simple regression equation, confidence interval, prediction interval, and required graphs. Insert tables and graphs in your report as appropriate.
Use Minitab and produce the appropriate output to answer the following questions. Attach the output.
-Estimate with 95% confidence the average power dissipation for all microprocessors with a speed of 200 MHz. Predict with 95% confidence the power dissipation for an individual microprocessor with a speed of 200 MHz. Write at least one sentence using your confidence interval and at least one sentence using your prediction interval.
-Verify that the p-value for the F is the same as the slope t statistic’s p-value, and show that t2 = F.
Microprocessor Speed and Heat Dissipation (n 14) Chip 1989 Intel 80486 1993 pentium 1997 Pentium II 1998 Intel Celeron 1999 Pentium IlI 1999 AMD Athlon 2000 Pentium 4 2004 Celeron D 2004 Pentium 4 2005 Pentium D 2007 AMD Phenom 2008 Intel Core 2 2009 Intel Core i7 2009 AMD Phenom IlI Source: New Scientist, Vol. 208, No. 2780, October 2, 2010, p. 41. Microprocessor Speed (MHz) Power Dissipation (watts) 20 100 233 300 600 600 1300 2100 3800 3200 2300 3200 2900 3200 10 35 20 42 50 51 73 115 130 95 136 95 125Explanation / Answer
The 95% confidence the average power dissipation for all microprocessors with a speed of 200 MHz is (10.63, 33.57). This CI tell us that the true average power dissipation for all microprocessors with a speed of 200 MHz will fall within (10.63, 33.57) with 95% confidence.
The predicted with 95% confidence the power dissipation for an individual microprocessor with a speed of 200 MHz is (-8.68, 52.88). It tells us that the expected value of power when the next speed data point is 200 MHz will fall within the (-8.68, 52.88) confidence interval with 95% confidence.
Output Results from Minitab.
The regression equation is
Power = 15.7 + 0.0319 Speed
Predictor Coef SE Coef T P
Constant 15.730 5.663 2.78 0.017
Speed 0.031853 0.002612 12.20 0.000
S = 13.1088 R-Sq = 92.5% R-Sq(adj) = 91.9%
Analysis of Variance
Source DF SS MS F P
Regression 1 25562 25562 148.75 0.000
Residual Error 12 2062 172
Total 13 27624
Predicted Values for New Observations
New Obs Fit SE Fit 95% CI 95% PI
1 22.10 5.26 (10.63, 33.57) (-8.68, 52.88)
Values of Predictors for New Observations
New Obs Speed
1 200
From the regression and ANOVA tables, the p-value of the slop of speed is 0.000 and the p-value of the F is 0.000. Hence, both the p-values are same. The t-value of speed from regression table is 12.20 with t^2=148.84 and the F-value is 148.75. Hence they are same after neglecting after point values.
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