![8. DeGroot&Shervish (2002) consider an experiment to study the combined effects of taking a stimulant and a tranquilizer. In this experiment three types of stimulant and four types of tranquilizer are administered to a group of rabbits. Each rabbit received one of the stimulants, then 20 minutes later, one of the tranquilizers. One hour later their response time (in microseconds) to a stimulus was measured. The results were: Tranquilizer Stimulant 1 11.20 7.40 7.10 9.60 11.60 8.10 7.00 7.60 2 12.70 10.30 8.80 11.30 14.00 7.90 8.50 10.80 3 10.10 5.50 5.00 6.50 9.60 6.90 7.30 5.70 Consider the model Use the attached R output to answer the following questions. You should adopt the convention that the interaction sum of squares is incorporated into the error sum of squares if the interaction is not significant. (a) Consider testing Ho : %,-0, i-1, 2, 3, j-1, 2, 3, 4, at the 5% level of significance. What is the value of the test statistic, its distribution when Ho is 121 true and the p-value of the test? (b) Consider testing Ho-ai-a2-a3 at the 5% level of significance, what is the value of the test statistic, its distribution when Ho is true and the p-value of [21 the test? (c) Consider testing H0 : β1 at the 5% level of significance. What is the value of the test statistic, its distribution when Ho is true and the p-value of the test? (d) Give a point estimate of the variance ơ2 (e) Briefly state your conclusions. 12]](http://img.homeworklib.com/questions/c24343e0-5124-11ea-a417-15e718750d10.png?x-oss-process=image/resize,w_560)
The R code will help to answer
the question.![11.6,8.1,7.0,7.6, 12.7,10.3,8.8,11.3, 14.0,7.9,8.5,10.8, 10.1,5.5,5.0,6.5 9.6,6.9,7.3,5.7); A <as.factor (rep(1:4,6)); Bas.factor (rep (1:3,each-8)); rbind (x,A,B) X 11.2 7.4 7.1 9.6 11.6 8.1 7 7.6 12.7 10.3 8.8 11.3 14 7.9 A 1.0 2.0 3.0 4.01.0 2.0 3 4.0 1.0 2.0 3.0 4.0 В 1.01.01.0 1.01.01.0 11.0 2.0 2.0 2.0 2.0 1 2.0 2 2.0 [,15] C,16] ,17 [,18] [,19] ,20] [,21] [,22] ,23] ,24] X 8.5 10.8 10.1 5.5 A 3.0 4.0 1.0 2.0 B 2.0 2.0 3.0 3.0 5 6.5 9.6 6.97.3 5.7 3 4.0 1.0 2.0 3.0 4.0 3.0 3.0 3.0 3.03.0 > anova(M.all); Analysis of Variance Table Response : X Df Sum Sq Mean Sq F value PrF) 66.371 22.1237 25.7878 1.617e-05 2 48.016 24.0079 27.9840 3.029e-05 6 3.627 0.6046 0.7047 0.6521 A: B Residuals 12 10.295 0.8579 Signif. codes: 00.0010.010.05 > M. 12 <-1n(X-A+B); > anova (M. 12) Analysis of Variance Table 01 1 Response : X Df Sum Sq Mean Sq F value Pr(>F) 6 3 66.371 22.1237 28.603 4.587e-07 2 48.016 24.0079 31.039 1.465e-06 Residuals 18 13.922 0.7735 Signif. codes : 0 , , 0.001 ,**, 0.01 ,*, 0.05 ,., 0.1 , , 1](http://img.homeworklib.com/questions/c2e75460-5124-11ea-95c4-a55caaf8eb99.png?x-oss-process=image/resize,w_560)
Homework Answers
This is a problem of two way Analysis Of Variance(ANOVA) with m
observations per cell.
Add Answer to:
The R code will help to answer the question. 8. DeGroot&Shervish (2002) consider an experiment to...
6. Consider the additive two way analysis of variance model where Σα:la.-012b1ßi = 0 and the...
6. Consider the additive two way analysis of variance model where Σα:la.-012b1ßi = 0 and the Eij are independent normal randonn vari- ables with zero means and variance ơ2.Let i-1 (a) Show that are unbiased estimators of the respective parameters. (b) (Devore, 1987) In an experiment to assess the effect of the angle of pull on the force required to separate electrical connectors, four different angles (factor A) were used and each of 5 connectors (factor B) were pulled once...
> summaryCls) Call: Lm(formula y X) Residuals: -0.20283 -0.146910.02255 0.06655 0.44541 Coefficients: (Intercept) 0.36510 0.09904 3.686...
> summaryCls) Call: Lm(formula y X) Residuals: -0.20283 -0.146910.02255 0.06655 0.44541 Coefficients: (Intercept) 0.36510 0.09904 3.686 0.003586 ** Min 1Q Median 3Q Max Estimate Std. Error t value Pr(>ltl) 0.96683 0.18292 5.286 0.000258*** Signif. codes: 00.001*0.010.050.11 Residual standard error: 0.1932 on 11 degrees of freedom Multiple R-squared 0.7175, Adjusted R-squared: 0.6918 F-statistic: 27.94 on 1 and 11 DF, p-value: 0.0002581 > anovaCls) Analysis of Variance Table Response : y Df Sum Sq Mean Sq F value PrOF) 1 1.04275 1.04275...
Using R output provided 1). Perform hypothesis testing for B(beta)1=2 using A(alpha)=0.05 > summary(ls) Call: Residuals:...
Using R output provided
1). Perform hypothesis testing for B(beta)1=2 using
A(alpha)=0.05
> summary(ls) Call: Residuals: Min 1Q Median 3Q Max 0.20283 -0.14691 -0.02255 0.06655 0.44541 Coefficients: (Intercept) 0.365100.099043.686 0.003586 ** Signif. codes: 0 '***' 0.001 '0.01 '*'0.05 '.' 0.1''1 Estimate Std. Error t value Pr>Itl) 0.96683 0.18292 5.286 0.000258** Residual standard error: 0.1932 on 11 degrees of freedom Multiple R-squared 0.7175, Adjusted R-squared: 0.6918 F-statistic: 27.94 on 1 and 11 DF, p-value: 0.0002581 anovaCLs) Analysis of Variance Table Response:...
Using the built in data in R “ToothGrowth”. Why factor(does) resulted in a different p-value using...
Using the built in data in R “ToothGrowth”. Why factor(does)
resulted in a different p-value using anova function.
headerH TRUE) 33 Corn <- factor(datal, 1]) 34 Yield <- datal, 21 35 Corn 36 table (Corn) 37 Yield 38 tapply(Yield, list (Corn) mean) group means 39 boxplot(Yield~datal,1]) 40 41 InsectSprays 42 table(InsectSprays) 43 Jungkook InsectSprays, 1] 44 Jungkook 45-Jin= InsectSprays [, 2] 46 Jin 47 boxplot (Jungkook-Jin) 48 49 pairwise.t.test(vield, Corn, pool.sd FALSE, p. adjust.method "none 50 Insectsprays 51 does 52...
(a) Using the above t-test data to determine whether or not there is a linear relationship...
(a) Using the above t-test data to determine whether or not there
is a linear relationship between the two variables.
(b) Using the above ANOVA F-test data to determine whether or not
there is a linear relationship between the two variables.
(c) How do the results in (a) compare to those in (b)?
We were unable to transcribe this imageAnalysis of Variance Table Response: DatSGPA Dat $ACT 1 3. 588 3. 5878 9. 2402 0.002917 Df Sum Sq Mean sq...
Analysis of Variance Table Response: Price Df Sum Sq Mean Sq F value Pr(>F) Living.Area 1 1.3501e+12 1.3501e+12 362.0394 < 2e-16 *** Bedrooms 1 2.3642e+10 2.3642e+10 6.3394 0.01241 * Fireplaces...
Analysis of Variance Table Response: Price Df Sum Sq Mean Sq F value Pr(>F) Living.Area 1 1.3501e+12 1.3501e+12 362.0394 < 2e-16 *** Bedrooms 1 2.3642e+10 2.3642e+10 6.3394 0.01241 * Fireplaces 1 7.6232e+07 7.6232e+07 0.0204 0.88642 Residuals 259 9.6588e+11 3.7293e+09 --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 > Using= 0.05, perform an F test of overall linear relationship. State the hypotheses, the value of F-test statistic, p-value, and your conclusion.
2. 2. After we fit the model, the R commander output is provided below. Coefficients: (Intercept)...
2. 2. After we fit the model, the R commander output is provided below. Coefficients: (Intercept) -5.128e+03 1.103e+02 46.49 2e-16** Estimate std. Brror t value Pr(lt|) TEMP PERT TEM: FERT 1.45se-01 9.692e-03 -15.01 1.06e-12 3.110e+01 1.344e+00 23.13 2e-16* 1.397e+02 3.140e+00 44.51 < 2e-16** TEMPSQ FERTSO -1.334e-01 6.853e-03 19.46 6.46e-15 -1.144e+00 2.741e-02 41.74 <2e-16 signif. codes: 00.001 0.01 0.05 011 Residual standard error: 1.679 on 21 degrees of freedom Multiple R-squared: 0.993, F-statistic: 596.3 on 5 and 21 DF, p-value: 2.2e-16...
write answer step by step on the paper What would you expect to see if you...
write answer step by step on the paper
What would you expect to see if you were to run the following code? Please describe th analysis and the result briefly. (20 pts) 5- > myANOVA <- aov(Learning" Group Condition) >summary(myANOVA) Group Condition Group:Condition Residuals Df Sum Sq 1.8454 1 0.1591 0.3164 59 1.3325 Mean Sq 1.84537 0.15910 0.31640 0.02258 F value 81.7106 7.0448 14.0100 Pr(>F) 9.822e-13** 0.0102017 0.000414*** Signif. codes:0.001*0.01' 0.05'0.1'"'1 > boxplot(Learning"Group"condition,col:c("#ffdddd","#ddddff"))
A company manager is interested in analyzing the relationship between years of working experience and the...
A company manager is interested in analyzing the relationship between years of working experience and the salary of their employees. He has collected the data from 30 employees of their years of experience and the salary. Below provided is a partial regression output from R. Use the provided information to answer below questions Coefficients: (Intercept) YearsExperience Estimate Std. Error t value Pr(>ltl) 25792.2 2273.1 9450.0 --- Signif. codes: O '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1'' 1 Analysis of...
· t0.025;3 = 3.182, to.025;4 = 2.776, 10.025:8 = 2.306 • F0.05;1,3 = 10.128, F0.05;1,4 =...
· t0.025;3 = 3.182, to.025;4 = 2.776, 10.025:8 = 2.306 • F0.05;1,3 = 10.128, F0.05;1,4 = 7.709, F0.05;1,8 = 5.318, F0.05;2,46 = 3.200, F0.05;3,46 = 2.807 • X2025;8 = 17.535, X3.975,8 = 2.180 2. (31 points) To investigate the effectiveness of allergy medication, ten patients were given varying doses of the allergy medication and asked to report back when the med ication seems to wear off. Assume that the simple linear regression model y = 30 + Bis is appropriate,...
6. Consider the additive two way analysis of variance model where Σα:la.-012b1ßi = 0 and the Eij are independent normal randonn vari- ables with zero means and variance ơ2.Let i-1 (a) Show that are unbiased estimators of the respective parameters. (b) (Devore, 1987) In an experiment to assess the effect of the angle of pull on the force required to separate electrical connectors, four different angles (factor A) were used and each of 5 connectors (factor B) were pulled once...
> summaryCls) Call: Lm(formula y X) Residuals: -0.20283 -0.146910.02255 0.06655 0.44541 Coefficients: (Intercept) 0.36510 0.09904 3.686 0.003586 ** Min 1Q Median 3Q Max Estimate Std. Error t value Pr(>ltl) 0.96683 0.18292 5.286 0.000258*** Signif. codes: 00.001*0.010.050.11 Residual standard error: 0.1932 on 11 degrees of freedom Multiple R-squared 0.7175, Adjusted R-squared: 0.6918 F-statistic: 27.94 on 1 and 11 DF, p-value: 0.0002581 > anovaCls) Analysis of Variance Table Response : y Df Sum Sq Mean Sq F value PrOF) 1 1.04275 1.04275...
Using R output provided
1). Perform hypothesis testing for B(beta)1=2 using
A(alpha)=0.05
> summary(ls) Call: Residuals: Min 1Q Median 3Q Max 0.20283 -0.14691 -0.02255 0.06655 0.44541 Coefficients: (Intercept) 0.365100.099043.686 0.003586 ** Signif. codes: 0 '***' 0.001 '0.01 '*'0.05 '.' 0.1''1 Estimate Std. Error t value Pr>Itl) 0.96683 0.18292 5.286 0.000258** Residual standard error: 0.1932 on 11 degrees of freedom Multiple R-squared 0.7175, Adjusted R-squared: 0.6918 F-statistic: 27.94 on 1 and 11 DF, p-value: 0.0002581 anovaCLs) Analysis of Variance Table Response:...
Using the built in data in R “ToothGrowth”. Why factor(does)
resulted in a different p-value using anova function.
headerH TRUE) 33 Corn <- factor(datal, 1]) 34 Yield <- datal, 21 35 Corn 36 table (Corn) 37 Yield 38 tapply(Yield, list (Corn) mean) group means 39 boxplot(Yield~datal,1]) 40 41 InsectSprays 42 table(InsectSprays) 43 Jungkook InsectSprays, 1] 44 Jungkook 45-Jin= InsectSprays [, 2] 46 Jin 47 boxplot (Jungkook-Jin) 48 49 pairwise.t.test(vield, Corn, pool.sd FALSE, p. adjust.method "none 50 Insectsprays 51 does 52...
(a) Using the above t-test data to determine whether or not there
is a linear relationship between the two variables.
(b) Using the above ANOVA F-test data to determine whether or not
there is a linear relationship between the two variables.
(c) How do the results in (a) compare to those in (b)?
We were unable to transcribe this imageAnalysis of Variance Table Response: DatSGPA Dat $ACT 1 3. 588 3. 5878 9. 2402 0.002917 Df Sum Sq Mean sq...
2. 2. After we fit the model, the R commander output is provided below. Coefficients: (Intercept) -5.128e+03 1.103e+02 46.49 2e-16** Estimate std. Brror t value Pr(lt|) TEMP PERT TEM: FERT 1.45se-01 9.692e-03 -15.01 1.06e-12 3.110e+01 1.344e+00 23.13 2e-16* 1.397e+02 3.140e+00 44.51 < 2e-16** TEMPSQ FERTSO -1.334e-01 6.853e-03 19.46 6.46e-15 -1.144e+00 2.741e-02 41.74 <2e-16 signif. codes: 00.001 0.01 0.05 011 Residual standard error: 1.679 on 21 degrees of freedom Multiple R-squared: 0.993, F-statistic: 596.3 on 5 and 21 DF, p-value: 2.2e-16...
write answer step by step on the paper
What would you expect to see if you were to run the following code? Please describe th analysis and the result briefly. (20 pts) 5- > myANOVA <- aov(Learning" Group Condition) >summary(myANOVA) Group Condition Group:Condition Residuals Df Sum Sq 1.8454 1 0.1591 0.3164 59 1.3325 Mean Sq 1.84537 0.15910 0.31640 0.02258 F value 81.7106 7.0448 14.0100 Pr(>F) 9.822e-13** 0.0102017 0.000414*** Signif. codes:0.001*0.01' 0.05'0.1'"'1 > boxplot(Learning"Group"condition,col:c("#ffdddd","#ddddff"))
A company manager is interested in analyzing the relationship between years of working experience and the salary of their employees. He has collected the data from 30 employees of their years of experience and the salary. Below provided is a partial regression output from R. Use the provided information to answer below questions Coefficients: (Intercept) YearsExperience Estimate Std. Error t value Pr(>ltl) 25792.2 2273.1 9450.0 --- Signif. codes: O '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1'' 1 Analysis of...
· t0.025;3 = 3.182, to.025;4 = 2.776, 10.025:8 = 2.306 • F0.05;1,3 = 10.128, F0.05;1,4 = 7.709, F0.05;1,8 = 5.318, F0.05;2,46 = 3.200, F0.05;3,46 = 2.807 • X2025;8 = 17.535, X3.975,8 = 2.180 2. (31 points) To investigate the effectiveness of allergy medication, ten patients were given varying doses of the allergy medication and asked to report back when the med ication seems to wear off. Assume that the simple linear regression model y = 30 + Bis is appropriate,...
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