Also Obtain Bonferroni joint confidence intervals for b0 and b1, using a 95 perc

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Obtain Bonferroni joint confidence intervals for b0 and b1, using a 95 percent
family confidence coefficient. Interpret your confidence intervals.

3. Plastic hardness. Sixteen batches of the plastic were made, and from each batch one test item was molded. Each test item was randomly assigned to one of the four predetermined time levels, and the hardness was measured after the assigned elapsed time. The results are shown below; X is the elapsed time in hours, and Y is hardness in Brinell units. Assume that first-order-regression model Y - Po+B1X e is appropriate. i: 23 .14 15 16 ...40 40 40 Y: 199 205 196 248 253 246 X 16 16 16 In addition to X = 28 and 225.5625, the summary of the fitted model is given below: Call In(formula y ” x) Residuals Min 1Q Median 3Q Max -5.1500-2.2188 0.1625 2.6875 5.5750 Coefficients Estimate Std. Error t value Pr>ltl) (Intercept) 168.60000 2.65702 63.45 2e-16* 2.03438 0.09039 22.51 2.16e-12 Signif. codes: 00.001 **0.010.05 0.1 1 Residual standard error: 3.234 on 14 degrees of freedom Multiple R-squared: 0. F-statistic: 506.5 on 1 and 14 DF 9731 Adjusted R-squared: 0.9712 ,p-value: 2.159e-12 a) Will bo and bi tend to err in the same direction or in opposite direction here? 10 Points Explain.

Explanation / Answer

same direction

y<- c( 199,205,196,200,218,220,215,223,237,234,235,230,250,248,253,246)
> x <- c(16,16,16,16,24,24,24,24,32,32,32,32,40,40,40,40)
> mod <- lm(y~x)
> summary(mod)

Call:
lm(formula = y ~ x)

Residuals:
    Min      1Q Median      3Q     Max
-5.1500 -2.2188 0.1625 2.6875 5.5750

Coefficients:
             Estimate Std. Error t value Pr(>|t|)  
(Intercept) 168.60000    2.65702   63.45 < 2e-16 ***
x             2.03438    0.09039   22.51 2.16e-12 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 3.234 on 14 degrees of freedom
Multiple R-squared: 0.9731,    Adjusted R-squared: 0.9712
F-statistic: 506.5 on 1 and 14 DF, p-value: 2.159e-12

Bonferroni joint confidence intervals for b1

confint(mod, 'x', level = 0.975)
        1.25 %      98.75 %
x    1.807526    2.261224

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