Stat 21 18-Homework 3 Question 1 a) For the data in Homework 2, Question 1, calc

Question

Stat 21 18-Homework 3 Question 1 a) For the data in Homework 2, Question 1, calculate the ANOVA table. Use the ANOVA Table to conduct an F-Test to see if the model is significant (use = 0.05). b) Give a 95% confidence interval for the mean absorption when the concentration level is 10. c) Give a 95% prediction interval for the absorption level for an individual protein whose concentration level is 10. d) For the data in Homework 2, Question 2, calculate the ANOVA table for the data. Use the ANOVA Table to conduct an F-Test to see if the model is significant (use -0.05).

Explanation / Answer

a)

x <- c(4 ,6,8,10,12,14,16)
> y <- c(10,15,18,18,24,22,26)
> model = lm (y~x)
> summary(model)

Call:
lm(formula = y ~ x)

Residuals:
      1       2       3       4       5       6       7
-1.7143 0.8571 1.4286 -1.0000 2.5714 -1.8571 -0.2857

Coefficients:
            Estimate Std. Error t value Pr(>|t|)  
(Intercept)   6.8571     1.8686   3.670 0.014450 *
x             1.2143     0.1735   6.999 0.000917 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 1.836 on 5 degrees of freedom
Multiple R-squared: 0.9074,    Adjusted R-squared: 0.8889
F-statistic: 48.98 on 1 and 5 DF, p-value: 0.0009175

b)

predict (model, data.frame(x = 10), interval = "confidence")
fit      lwr      upr
1 19 17.21602 20.78398

c)
> predict (model, data.frame(x = 10), interval = "prediction")
fit      lwr      upr
1 19 13.95415 24.04585

d)

ANOVA df SS MS F Significance F Regression 1 165.1428571 165.1428571 48.98305085 0.000917478 Residual 5 16.85714286 3.371428571 Total 6 182

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